absorber

By proposition 6.5.4, X is a skeletoid and hence an absorber by theorem 6.5.1.

1988, J. van Mill, Infinite-Dimensional Topology: Prerequisites and Introduction, page 285:

Skeletoids and absorbers play an important role in infinite-dimensional topology. The existence and uniqueness of skeletoids (and absorbers) with respect to certain collections allow one to study completely metrizable infinite-dimensional manifolds by using the technique of compact manifolds, incomplete manifolds by those of complete ones and so on.

2020, Howard Cook, Continua: With the Houston Problem Book, page 70:

(topology) A set that, under suitable transformations, can contain any set from a given class within a topological space.


open

en-adj

open (comparative more open or (phonetics) opener, superlative most open or (phonetics) openest)

more open (comparative)
opener (comparative)
most open (superlative)
openest (superlative)

closed-source

antonym(s) of “with a free license and no proprietary components”

Adjective from Middle English open, from Old English open (“open”), from Proto-West Germanic *opan, from Proto-Germanic *upanaz (“open”), from Proto-Indo-European *upo (“up from under, over”).
Cognates
* Scots apen (“open”)
* Saterland Frisian eepen (“open”)
* West Frisian iepen (“open”)
* Dutch open (“open”)
* Low German open, apen (“open”)
* German offen (“open”)
* Danish åben (“open”)
* Swedish öppen (“open”)
* Norwegian Bokmål åpen (“open”)
* Norwegian Nynorsk open (“open”)
* Icelandic opinn (“open”)
 Compare also Latin supinus (“on one's back, supine”), Albanian hap (“to open”). Related to up.
Verb from Middle English openen, from Old English openian (“to open”), from Proto-West Germanic *opanōn, from Proto-Germanic *upanōną (“to raise; lift; open”), from Proto-Germanic *upanaz (“open”, adjective). Cognate with Saterland Frisian eepenje (“to open”), West Frisian iepenje (“to open”), Dutch openen (“to open”), German öffnen (“to open”), Danish åbne (“to open”), Swedish öppna (“to open”), Norwegian Bokmål åpne (“to open”), Norwegian Nynorsk and Icelandic opna (“to open”). Related to English up.
Noun from Middle English open (“an aperture or opening”), from the verb. In the sports sense, however, a shortening of “open competition”.

inh

at church every time the doors swing open

(mathematics, topology, of a set) Which is part of a predefined collection of subsets of X, that defines a topological space on X.

obert

math: which is part of a predefined collection of subsets


chain

From Middle English cheyne, chaine, from Old French chaine, chaene (“chain”), from Latin catēna (“chain”), from Proto-Indo-European *kat- (“to braid, twist; hut, shed”). Doublet of catena. Displaced native Middle English rakil and rakent (from Old English racente (“chain”)); see rackan.

der

a chain is only as strong as its weakest link

(algebraic topology, originally) A formal sum of cells in a CW complex of a certain dimension k (in which case the formal sums are called k'''-chains); a formal sum of simplices or cubes of a certain dimension in a simplical complex or cubical complex (respectively).

(algebraic topology, homological algebra, more generally) An element of a group (or module) in a chain complex.


path

From Middle English path, peth, from Old English pæþ (“path, track”), from Proto-West Germanic *paþ, from Proto-Germanic *paþaz (“path”). The Proto-Germanic term is possibly borrowed from Iranian, from Proto-Iranian *pántaHh, from Proto-Indo-Iranian *pántaHs, from Proto-Indo-European *póntoh₁s, from the root *pent- (“to pass”), however this is disputed. Cognate with West Frisian paad, Dutch pad, German Pfad. Indo-Iranian cognates could be Avestan 𐬞𐬀𐬧𐬙𐬃 (paṇtā̊, “way”), Old Persian 𐎱𐎰 (p-θ /paθi/)), Sanskrit पन्था (panthā). See also English find). Doublet of panth.

lead someone down the garden path, lead someone up the garden path

(topology) A continuous map f from the unit interval I=[0,1] to a topological space X.


itu

itu (nominative singular)
idut (nominative plural)
itu (accusative nominative singular)
idut (accusative nominative plural)
idun (accusative genitive singular)
idut (accusative genitive plural)
idun (genitive singular)
itujen (genitive plural)
itua (partitive singular)
ituja (partitive plural)
idussa (inessive singular)
iduissa (inessive plural)
idusta (elative singular)
iduista (elative plural)
ituun (illative singular)
ituihin (illative plural)
idulla (adessive singular)
iduilla (adessive plural)
idulta (ablative singular)
iduilta (ablative plural)
idulle (allative singular)
iduille (allative plural)
ituna (essive singular)
ituina (essive plural)
iduksi (singular translative)
iduiksi (plural translative)
idutta (abessive singular)
iduitta (abessive plural)
iduin (instructive plural)
See the possessive forms below. (comitative)
ituni (nominative singular)
ituni (nominative plural)
ituni (accusative nominative singular)
ituni (accusative nominative plural)
ituni (accusative genitive singular)
ituni (accusative genitive plural)
ituni (genitive singular)
itujeni (genitive plural)
ituani (partitive singular)
itujani (partitive plural)
idussani (inessive singular)
iduissani (inessive plural)
idustani (elative singular)
iduistani (elative plural)
ituuni (illative singular)
ituihini (illative plural)
idullani (adessive singular)
iduillani (adessive plural)
idultani (ablative singular)
iduiltani (ablative plural)
idulleni (allative singular)
iduilleni (allative plural)
itunani (essive singular)
ituinani (essive plural)
idukseni (singular translative)
iduikseni (plural translative)
iduttani (abessive singular)
iduittani (abessive plural)
ituineni (comitative plural)
itusi (nominative singular)
itusi (nominative plural)
itusi (accusative nominative singular)
itusi (accusative nominative plural)
itusi (accusative genitive singular)
itusi (accusative genitive plural)
itusi (genitive singular)
itujesi (genitive plural)
ituasi (partitive singular)
itujasi (partitive plural)
idussasi (inessive singular)
iduissasi (inessive plural)
idustasi (elative singular)
iduistasi (elative plural)
ituusi (illative singular)
ituihisi (illative plural)
idullasi (adessive singular)
iduillasi (adessive plural)
idultasi (ablative singular)
iduiltasi (ablative plural)
idullesi (allative singular)
iduillesi (allative plural)
itunasi (essive singular)
ituinasi (essive plural)
iduksesi (singular translative)
iduiksesi (plural translative)
iduttasi (abessive singular)
iduittasi (abessive plural)
ituinesi (comitative plural)
itumme (nominative singular)
itumme (nominative plural)
itumme (accusative nominative singular)
itumme (accusative nominative plural)
itumme (accusative genitive singular)
itumme (accusative genitive plural)
itumme (genitive singular)
itujemme (genitive plural)
ituamme (partitive singular)
itujamme (partitive plural)
idussamme (inessive singular)
iduissamme (inessive plural)
idustamme (elative singular)
iduistamme (elative plural)
ituumme (illative singular)
ituihimme (illative plural)
idullamme (adessive singular)
iduillamme (adessive plural)
idultamme (ablative singular)
iduiltamme (ablative plural)
idullemme (allative singular)
iduillemme (allative plural)
itunamme (essive singular)
ituinamme (essive plural)
iduksemme (singular translative)
iduiksemme (plural translative)
iduttamme (abessive singular)
iduittamme (abessive plural)
ituinemme (comitative plural)
itunne (nominative singular)
itunne (nominative plural)
itunne (accusative nominative singular)
itunne (accusative nominative plural)
itunne (accusative genitive singular)
itunne (accusative genitive plural)
itunne (genitive singular)
itujenne (genitive plural)
ituanne (partitive singular)
itujanne (partitive plural)
idussanne (inessive singular)
iduissanne (inessive plural)
idustanne (elative singular)
iduistanne (elative plural)
ituunne (illative singular)
ituihinne (illative plural)
idullanne (adessive singular)
iduillanne (adessive plural)
idultanne (ablative singular)
iduiltanne (ablative plural)
idullenne (allative singular)
iduillenne (allative plural)
itunanne (essive singular)
ituinanne (essive plural)
iduksenne (singular translative)
iduiksenne (plural translative)
iduttanne (abessive singular)
iduittanne (abessive plural)
ituinenne (comitative plural)
itunsa (nominative singular)
itunsa (nominative plural)
itunsa (accusative nominative singular)
itunsa (accusative nominative plural)
itunsa (accusative genitive singular)
itunsa (accusative genitive plural)
itunsa (genitive singular)
itujensa (genitive plural)
ituaan (partitive singular)
ituansa (partitive singular)
itujaan (partitive plural)
itujansa (partitive plural)
idussaan (inessive singular)
idussansa (inessive singular)
iduissaan (inessive plural)
iduissansa (inessive plural)
idustaan (elative singular)
idustansa (elative singular)
iduistaan (elative plural)
iduistansa (elative plural)
ituunsa (illative singular)
ituihinsa (illative plural)
idullaan (adessive singular)
idullansa (adessive singular)
iduillaan (adessive plural)
iduillansa (adessive plural)
idultaan (ablative singular)
idultansa (ablative singular)
iduiltaan (ablative plural)
iduiltansa (ablative plural)
idulleen (allative singular)
idullensa (allative singular)
iduilleen (allative plural)
iduillensa (allative plural)
itunaan (essive singular)
itunansa (essive singular)
ituinaan (essive plural)
ituinansa (essive plural)
idukseen (singular translative)
iduksensa (singular translative)
iduikseen (plural translative)
iduiksensa (plural translative)
iduttaan (abessive singular)
iduttansa (abessive singular)
iduittaan (abessive plural)
iduittansa (abessive plural)
ituineen (comitative plural)
ituinensa (comitative plural)

From Proto-Finnic *itu (compare Estonian idu), derived from itää; equivalent to itää (“to sprout, germinate”) + -u.


braid

en-noun

braid (countable and uncountable, plural braids)

braids (plural)
brayde (alternative obsolete)
breyde (alternative obsolete)
broid (alternative obsolete)

From Middle English braiden, breided, bræiden, from Old English breġdan (“to move quickly, pull, shake, swing, throw (wrestling), draw (sword), drag; bend, weave, braid, knit, join together; change color, vary, be transformed; bind, knot; move, be pulled; flash”), from Proto-West Germanic *bregdan, from Proto-Germanic *bregdaną (“to flicker, flutter, jerk, tug, twitch, flinch, move, swing”), from Proto-Indo-European *bʰrēḱ-, *bʰrēǵ- (“to shine, shimmer”).
Cognate with Scots Scots brade, Scots braid (“to move quickly or suddenly”), Saterland Frisian braidje (“to knit”), West Frisian breidzje, Dutch breien (“to knit”), Low German breiden, German breiden, Bavarian bretten (“to move quickly, twitch”), Icelandic bregða (“to move quickly, jerk”), Faroese bregða (“to move quickly, react swiftly; to draw (sword)”) and Faroese bregda (“to plaid, braid, twist, twine”).

cog

We introduce braids via their historical roots and uses, make connections with knot theory and present the mathematical theory of braids through the braid group.

2009, Mitchell A. Berger, Louis H. Kauffman, Renzo L. Ricca, Lectures on Topological Fluid Mechanics, page 1:

In order to characterise the structure and complexity of a braid different numbers or topological invariants can be calculated.

2012, A. T. Skjeltorp, Tamas Vicsek, Complexity from Microscopic to Macroscopic Scales, page 144:

(mathematics, topology) Given two sets of n points on corresponding positions on two parallel lines, a braid is a unique set of crossings (over or under) between n strands that connect each point on one line to a point on the other line such that all points represent the terminus of one and only one strand and the traversal of any strand from a starting point to an ending point never moves further away from the from the ending point.


interior

/ɪnˈtɪə.ɹɪ.ə/

From Latin interior (“inner, interior”).

(mathematics, topology) The set of all interior points of a set.


weight

en-noun

weight (countable and uncountable, plural weights)

weights (plural)
wt. (alternative)
waight (alternative obsolete)

Belizean Creole: wayt

→ Japanese: ウエイト (ueito)

→ Burmese: ဝိတ် (wit)

From Middle English weight, weiȝte, weght, wight, from Old English wiht, ġewiht (“weight”), from Proto-Germanic *wihtiz ("weight"; compare *weganą (“to move”)), from Proto-Indo-European *weǵʰ- (“to move; pull; draw; drive”). Equivalent to weigh + -th (abstract nominal suffix).
Cognate with Scots wecht, weicht (“weight”), Saterland Frisian Wächte (“scale”), Gewicht (“weight”), West Frisian gewicht (“weight”), Dutch gewicht (“weight”), German Low German Wicht, Gewicht (“weight”), German Wucht (“massiveness, force”), Gewicht (“weight”).

gloss

"weight"; compare <i class="Latn mention" lang="gem-pro">*weganą</i> (“to move”)

inh

(topology) The smallest cardinality of a base.

paino

topology: the smallest cardinality of a base


curve

Attested since the 1690s, from Latin curvus (“bent, curved”), ultimately from Proto-Indo-European *(s)ker- (“to bend, curve, turn”) + *-wós. Doublet of curb, shrink, carcer, and cancer.


base

en-noun

base (countable and uncountable, plural bases)

acid

antonym(s) of “chemical compound that will neutralize an alkali”

From Middle English base, bas, baas, from Old French base, from Latin basis, from Ancient Greek βάσις (básis). Doublet of basis and bass.

أَسَاس

something from which other things extend

basis

chemical compound that will neutralize an acid

(topology) The set of sets from which a topology is generated.

база

topology: set of sets from which a topology is derived

(topology) A topological space, looked at in relation to one of its covering spaces, fibrations, or bundles.

kanta

topology: topological space, looked at in relation to one of its covering spaces, fibrations, or bundles


cover

cover (countable and uncountable, plural covers)

→ Hijazi Arabic: كَڤَر (kavar)

→ Portuguese: cover

Etymology tree
Proto-Indo-European *ḱe-?
Proto-Indo-European *ḱóm
Proto-Italic *kom
Old Latin com
Latin cum
Latin con-
Proto-Indo-European *h₁epi
Proto-Indo-European *h₂wer-
Proto-Indo-European *-yeti
Latin operiō
Latin cooperiō
Old French covrirbor.
Middle English coveren
English cover
From Middle English coveren, borrowed from Old French covrir, cueuvrir (modern French couvrir), from Late Latin coperire, from Latin cooperiō (“I cover completely”), from co- (intensive prefix) + operiō (“I close, cover”). Displaced native Middle English thecchen and bethecchen (“to cover”) (from Old English þeccan, beþeccan (“to cover”)), Middle English helen, (over)helen, (for)helen (“to cover, conceal”) (from Old English helan (“to conceal, cover, hide”)), Middle English wrien, (be)wreon (“to cover”) (from Old English (be)wrēon (“to cover”)), Middle English hodren, hothren (“to cover up”) (from Low German hudren (“to cover up”)).
According to the Oxford English Dictionary, the original sense of the verb and noun cover was “hide from view” as in its cognate covert. Except in the limited sense of “cover again”, the word recover is unrelated and is cognate with recuperate. Cognate with Spanish cubrir (“to cover”).

cog

throw nickels around like manhole covers

The open intervals are a cover for the real numbers.

(combinatorics, topology) A collection (or family) of subsets of a given set, whose union contains every element of said original set.


basis

en-noun

basis (plural bases or (rare) baseis or (nonstandard) basises)

bases (plural)
baseis (plural rare)
basises (nonstandard plural)

From Latin basis, from Ancient Greek βάσις (básis), from Proto-Indo-European *gʷémtis, derived from Proto-Indo-European *gʷem- (whence also come). Doublet of base.

The collection of all possible unions of basis elements of a basis is said to be the topology generated by that basis.

(topology) A collection of subsets ("basis elements") of a set, such that this collection covers the set, and for any two basis elements which both contain an element of the set, there is a third basis element contained in the intersection of the first two, which also contains that element.


handle

desctree

→ Japanese: ハンドル (handoru)
→ Hokkien: 捍多路 (hăn-tó͘-luh)
→ Sakizaya: handulu

From Middle English handel, handle, from Old English handle (“a handle”), from handlian (“to handle, feel, deal with, discuss”). See verb below. Cognate with Danish handel (“a handle”).

Such a 2-handle cancels the 1-handle so the manifold is D⁴.

2003, Gordana Matić, Clint McCrory, Topology and geometry of manifolds, →ISBN, page 182:

(topology) A topological space homeomorphic to a ball but viewed as a product of two lower-dimensional balls.


domain

range

antonym(s) of “domain of definition of a function”

From Middle English demayne, demain (“rule”), from Old French demeine, demaine, demeigne, domaine (“power”), (French domaine), from Latin dominium (“property, right of ownership”), from dominus (“master, proprietor, owner”). See dame, and compare demain, danger, dungeon. Doublet of demesne, domino.

definisieversameling

(mathematics) the set on which a function is defined

mathematical analysis
mathematical analysis

(mathematics, topology, mathematical analysis) An open and connected set in some topology. For example, the interval (0,1) as a subset of the real numbers.


suspension

en-noun

suspension (countable and uncountable, plural suspensions)

Borrowed from Late Latin suspensiōnem (“arching, vaulting; suspension”), from suspendēre (“to hang up, to suspend”), from sub- (“under”) + pendere (“to hang, to suspend”), from Proto-Italic *pendō (“to hang, to put in a hanging position”), from Proto-Indo-European *(s)pénd-e-ti, from *(s)pend- (“to pull; to spin”)). Compare Anglo-Norman suspensiun, French suspension, Occitan suspensio.

der

To get an intuitive feeling for the characteristics of H'-spaces, it is instructive to consider an important class of such spaces, the suspensions. The suspension of an arbitrary topological space Y is defined to be the quotient space of Y#92;timesI where Y#92;times 0 is identified to one point and Y#92;times 1 is identified to another point. For example, the suspension of a circle is a cylinder with the two ends collapsed into one point each; in other words, a space homeomorphic to a sphere.

2012, H. Rasmussen, “Strategy-proofness of Continuous Aggregation Maps”, in Geoffrey M. Heal, editor, Topological Social Choice: With 45 Figures (Social Choice and Welfare; vol. 14, no. 2, 1997), Berlin: Springer-Verlag, →DOI, →ISBN, page 110:

(topology) A topological space derived from another by taking the product of the original space with an interval and collapsing each end of the product to a point.

suspensie

topology: A topological space derived from another by taking the product of the original space with an interval and collapsing each end of the product to a point

A model category is called pointed if the initial object and terminal object are the same. The homotopy category of any pointed model category acquires a suspension functor denoted by #92;Sigma. It turns out that #92;text#123;Ho#125;(M) is a pre-triangulated category in a natural way[…]. When the suspension is an equivalence, M is called a stable model category, and in this case #92;text#123;Ho#125;(M) becomes a triangulated category[…].

2010, Paul Arne Østvær, “Preliminaries”, in Homotopy Theory of C*-Algebras (Frontiers in Mathematics), Basel: Birkhäuser, Springer Basel, →DOI, →ISBN, page 17:

(topology) A function derived, in a standard way, from another, such that the instant function’s domain and codomain are suspensions of the original function’s.

suspensie

topology: A function derived, in a standard way, from another, such that the instant function’s domain and codomain are suspensions of the original function’s


cycle

→ Japanese: サイクル (saikuru)

From Middle English cicle (“fixed length period of years”), from Late Latin cyclus, from Ancient Greek κύκλος (kúklos, “circle”), from Proto-Hellenic *kúklos, *kʷókʷlos, from Proto-Indo-European *kʷékʷlos (“circle, wheel”).
Doublet of chakra, chakram, charkha, chukker, cyclus, and wheel (see there for more).

pyörä

bicycle, tricycle, motorcycle etc. — see also bicycle

(topology, algebraic topology) A chain whose boundary is zero.


discrete

en-adj

discrete (comparative more discrete, superlative most discrete)

more discrete (comparative)
most discrete (superlative)

From Old French discret, from Latin discrētus, past participle of discernō (“divide”), from dis- + cernō (“sift”). Doublet of discreet.

(topology) Having each singleton subset open: said of a topological space or a topology.


graph

Clipping of graphic formula. From 1878; verb from 1889.

2008, Unnamed translators (AMS), A. V. Alexeevski, S. M. Natanzon, Hurwitz Numbers for Regular Coverings of Surfaces by Seamed Surfaces and Cardy-Frobenius Algebras of Finite Groups, V. M. Buchstaber, I. M. Krichever (editors), Geometry, Topology, and Mathematical Physics: S.P. Novikov's Seminar, 2006-2007, American Mathematical Society, page 6,
First, let us define its 1-dimensional analog, that is, a topological graph. A graph Δ is a 1-dimensional stratified topological space with finitely many 0-strata (vertices) and finitely many 1-strata (edges). […] A graph such that any vertex belongs to at least two half-edges we call an s-graph. Clearly the boundary ∂Ω of a surface Ω with marked points is an s-graph.
A morphism of graphs φ:Δ'→Δ is a continuous epimorphic map of graphs compatible with the stratification; i.e., the restriction of φ to any open 1-stratum (interior of an edge) of Δ' is a local (therefore, global) homeomorphism with appropriate open 1-stratum of Δ.

(topology) A topological space which represents some graph (ordered pair of sets) and which is constructed by representing the vertices as points and the edges as copies of the real interval [0,1] (where, for any given edge, 0 and 1 are identified with the points representing the two vertices) and equipping the result with a particular topology called the graph topology.


genus

en-noun

genus (plural genera or (all nonstandard) genuses or genusses or genii)

genera (plural)
genuses (nonstandard plural)
genusses (nonstandard plural)
genii (nonstandard plural)

→ Malayalam: ജീനസ് (jīnasŭ)

→ Swahili: jenasi

→ Thai: สกุล (sà-gun) (semantic loan)

Etymology tree
Proto-Indo-European *ǵenh₁-
Proto-Indo-European *-os
Proto-Indo-European *ǵénh₁os
Latin genusbor.
English genus
Borrowed from Latin genus (“birth, origin, a race, sort, kind”) from the root gen- in Latin gignō (“to beget, produce”). Doublet of gender and genre, further related to kin.

genus

rank in a taxonomic classification between family and species

(topology, graph theory, algebraic geometry) A natural number representing any of several related measures of the complexity of a given manifold or graph.


genus

genus (nominative singular)
genukset (nominative plural)
genus (accusative nominative singular)
genukset (accusative nominative plural)
genuksen (accusative genitive singular)
genukset (accusative genitive plural)
genuksen (genitive singular)
genusten (genitive plural)
genuksien (genitive plural)
genusta (partitive singular)
genuksia (partitive plural)
genuksessa (inessive singular)
genuksissa (inessive plural)
genuksesta (elative singular)
genuksista (elative plural)
genukseen (illative singular)
genuksiin (illative plural)
genuksella (adessive singular)
genuksilla (adessive plural)
genukselta (ablative singular)
genuksilta (ablative plural)
genukselle (allative singular)
genuksille (allative plural)
genuksena (essive singular)
genuksina (essive plural)
genukseksi (singular translative)
genuksiksi (plural translative)
genuksetta (abessive singular)
genuksitta (abessive plural)
genuksin (instructive plural)
See the possessive forms below. (comitative)
genukseni (nominative singular)
genukseni (nominative plural)
genukseni (accusative nominative singular)
genukseni (accusative nominative plural)
genukseni (accusative genitive singular)
genukseni (accusative genitive plural)
genukseni (genitive singular)
genusteni (genitive plural)
genuksieni (genitive plural)
genustani (partitive singular)
genuksiani (partitive plural)
genuksessani (inessive singular)
genuksissani (inessive plural)
genuksestani (elative singular)
genuksistani (elative plural)
genukseeni (illative singular)
genuksiini (illative plural)
genuksellani (adessive singular)
genuksillani (adessive plural)
genukseltani (ablative singular)
genuksiltani (ablative plural)
genukselleni (allative singular)
genuksilleni (allative plural)
genuksenani (essive singular)
genuksinani (essive plural)
genuksekseni (singular translative)
genuksikseni (plural translative)
genuksettani (abessive singular)
genuksittani (abessive plural)
genuksineni (comitative plural)
genuksesi (nominative singular)
genuksesi (nominative plural)
genuksesi (accusative nominative singular)
genuksesi (accusative nominative plural)
genuksesi (accusative genitive singular)
genuksesi (accusative genitive plural)
genuksesi (genitive singular)
genustesi (genitive plural)
genuksiesi (genitive plural)
genustasi (partitive singular)
genuksiasi (partitive plural)
genuksessasi (inessive singular)
genuksissasi (inessive plural)
genuksestasi (elative singular)
genuksistasi (elative plural)
genukseesi (illative singular)
genuksiisi (illative plural)
genuksellasi (adessive singular)
genuksillasi (adessive plural)
genukseltasi (ablative singular)
genuksiltasi (ablative plural)
genuksellesi (allative singular)
genuksillesi (allative plural)
genuksenasi (essive singular)
genuksinasi (essive plural)
genukseksesi (singular translative)
genuksiksesi (plural translative)
genuksettasi (abessive singular)
genuksittasi (abessive plural)
genuksinesi (comitative plural)
genuksemme (nominative singular)
genuksemme (nominative plural)
genuksemme (accusative nominative singular)
genuksemme (accusative nominative plural)
genuksemme (accusative genitive singular)
genuksemme (accusative genitive plural)
genuksemme (genitive singular)
genustemme (genitive plural)
genuksiemme (genitive plural)
genustamme (partitive singular)
genuksiamme (partitive plural)
genuksessamme (inessive singular)
genuksissamme (inessive plural)
genuksestamme (elative singular)
genuksistamme (elative plural)
genukseemme (illative singular)
genuksiimme (illative plural)
genuksellamme (adessive singular)
genuksillamme (adessive plural)
genukseltamme (ablative singular)
genuksiltamme (ablative plural)
genuksellemme (allative singular)
genuksillemme (allative plural)
genuksenamme (essive singular)
genuksinamme (essive plural)
genukseksemme (singular translative)
genuksiksemme (plural translative)
genuksettamme (abessive singular)
genuksittamme (abessive plural)
genuksinemme (comitative plural)
genuksenne (nominative singular)
genuksenne (nominative plural)
genuksenne (accusative nominative singular)
genuksenne (accusative nominative plural)
genuksenne (accusative genitive singular)
genuksenne (accusative genitive plural)
genuksenne (genitive singular)
genustenne (genitive plural)
genuksienne (genitive plural)
genustanne (partitive singular)
genuksianne (partitive plural)
genuksessanne (inessive singular)
genuksissanne (inessive plural)
genuksestanne (elative singular)
genuksistanne (elative plural)
genukseenne (illative singular)
genuksiinne (illative plural)
genuksellanne (adessive singular)
genuksillanne (adessive plural)
genukseltanne (ablative singular)
genuksiltanne (ablative plural)
genuksellenne (allative singular)
genuksillenne (allative plural)
genuksenanne (essive singular)
genuksinanne (essive plural)
genukseksenne (singular translative)
genuksiksenne (plural translative)
genuksettanne (abessive singular)
genuksittanne (abessive plural)
genuksinenne (comitative plural)
genuksensa (nominative singular)
genuksensa (nominative plural)
genuksensa (accusative nominative singular)
genuksensa (accusative nominative plural)
genuksensa (accusative genitive singular)
genuksensa (accusative genitive plural)
genuksensa (genitive singular)
genustensa (genitive plural)
genuksiensa (genitive plural)
genustaan (partitive singular)
genustansa (partitive singular)
genuksiaan (partitive plural)
genuksiansa (partitive plural)
genuksessaan (inessive singular)
genuksessansa (inessive singular)
genuksissaan (inessive plural)
genuksissansa (inessive plural)
genuksestaan (elative singular)
genuksestansa (elative singular)
genuksistaan (elative plural)
genuksistansa (elative plural)
genukseensa (illative singular)
genuksiinsa (illative plural)
genuksellaan (adessive singular)
genuksellansa (adessive singular)
genuksillaan (adessive plural)
genuksillansa (adessive plural)
genukseltaan (ablative singular)
genukseltansa (ablative singular)
genuksiltaan (ablative plural)
genuksiltansa (ablative plural)
genukselleen (allative singular)
genuksellensa (allative singular)
genuksilleen (allative plural)
genuksillensa (allative plural)
genuksenaan (essive singular)
genuksenansa (essive singular)
genuksinaan (essive plural)
genuksinansa (essive plural)
genuksekseen (singular translative)
genukseksensa (singular translative)
genuksikseen (plural translative)
genuksiksensa (plural translative)
genuksettaan (abessive singular)
genuksettansa (abessive singular)
genuksittaan (abessive plural)
genuksittansa (abessive plural)
genuksineen (comitative plural)
genuksinensa (comitative plural)


infinity

en-noun

infinity (countable and uncountable, plural infinities)

From Middle English infinite, from Old French infinité, from Latin īnfīnitās (“unlimitedness”), from negative prefix in- (“not”), + fīnis (“end”), + noun of state suffix -tās.

(countable, topology, mathematical analysis) An idealised point which is said to be approached by sequences of values whose magnitudes increase without bound.


closed

(topology, of a set) Having an open complement.


torus

Borrowed from Latin torus (“a round, swelling, elevation, protuberance”).

bor

A 4-variable Karnaugh map can be thought of, topologically, as being a torus.

(geometry) The standard representation of such a space in 3-dimensional Euclidean space: a surface or solid formed by rotating a closed curve, especially a circle, about a line which lies in the same plane but does not intersect it (e.g. like a ring doughnut).

(topology) A topological space which is a product of two circles.

(topology, in combination, n-torus, 4-torus, etc.) The product of the specified number of circles.


torus

torus (nominative singular)
torukset (nominative plural)
torus (accusative nominative singular)
torukset (accusative nominative plural)
toruksen (accusative genitive singular)
torukset (accusative genitive plural)
toruksen (genitive singular)
torusten (genitive plural)
toruksien (genitive plural)
torusta (partitive singular)
toruksia (partitive plural)
toruksessa (inessive singular)
toruksissa (inessive plural)
toruksesta (elative singular)
toruksista (elative plural)
torukseen (illative singular)
toruksiin (illative plural)
toruksella (adessive singular)
toruksilla (adessive plural)
torukselta (ablative singular)
toruksilta (ablative plural)
torukselle (allative singular)
toruksille (allative plural)
toruksena (essive singular)
toruksina (essive plural)
torukseksi (singular translative)
toruksiksi (plural translative)
toruksetta (abessive singular)
toruksitta (abessive plural)
toruksin (instructive plural)
See the possessive forms below. (comitative)
torukseni (nominative singular)
torukseni (nominative plural)
torukseni (accusative nominative singular)
torukseni (accusative nominative plural)
torukseni (accusative genitive singular)
torukseni (accusative genitive plural)
torukseni (genitive singular)
torusteni (genitive plural)
toruksieni (genitive plural)
torustani (partitive singular)
toruksiani (partitive plural)
toruksessani (inessive singular)
toruksissani (inessive plural)
toruksestani (elative singular)
toruksistani (elative plural)
torukseeni (illative singular)
toruksiini (illative plural)
toruksellani (adessive singular)
toruksillani (adessive plural)
torukseltani (ablative singular)
toruksiltani (ablative plural)
torukselleni (allative singular)
toruksilleni (allative plural)
toruksenani (essive singular)
toruksinani (essive plural)
toruksekseni (singular translative)
toruksikseni (plural translative)
toruksettani (abessive singular)
toruksittani (abessive plural)
toruksineni (comitative plural)
toruksesi (nominative singular)
toruksesi (nominative plural)
toruksesi (accusative nominative singular)
toruksesi (accusative nominative plural)
toruksesi (accusative genitive singular)
toruksesi (accusative genitive plural)
toruksesi (genitive singular)
torustesi (genitive plural)
toruksiesi (genitive plural)
torustasi (partitive singular)
toruksiasi (partitive plural)
toruksessasi (inessive singular)
toruksissasi (inessive plural)
toruksestasi (elative singular)
toruksistasi (elative plural)
torukseesi (illative singular)
toruksiisi (illative plural)
toruksellasi (adessive singular)
toruksillasi (adessive plural)
torukseltasi (ablative singular)
toruksiltasi (ablative plural)
toruksellesi (allative singular)
toruksillesi (allative plural)
toruksenasi (essive singular)
toruksinasi (essive plural)
torukseksesi (singular translative)
toruksiksesi (plural translative)
toruksettasi (abessive singular)
toruksittasi (abessive plural)
toruksinesi (comitative plural)
toruksemme (nominative singular)
toruksemme (nominative plural)
toruksemme (accusative nominative singular)
toruksemme (accusative nominative plural)
toruksemme (accusative genitive singular)
toruksemme (accusative genitive plural)
toruksemme (genitive singular)
torustemme (genitive plural)
toruksiemme (genitive plural)
torustamme (partitive singular)
toruksiamme (partitive plural)
toruksessamme (inessive singular)
toruksissamme (inessive plural)
toruksestamme (elative singular)
toruksistamme (elative plural)
torukseemme (illative singular)
toruksiimme (illative plural)
toruksellamme (adessive singular)
toruksillamme (adessive plural)
torukseltamme (ablative singular)
toruksiltamme (ablative plural)
toruksellemme (allative singular)
toruksillemme (allative plural)
toruksenamme (essive singular)
toruksinamme (essive plural)
torukseksemme (singular translative)
toruksiksemme (plural translative)
toruksettamme (abessive singular)
toruksittamme (abessive plural)
toruksinemme (comitative plural)
toruksenne (nominative singular)
toruksenne (nominative plural)
toruksenne (accusative nominative singular)
toruksenne (accusative nominative plural)
toruksenne (accusative genitive singular)
toruksenne (accusative genitive plural)
toruksenne (genitive singular)
torustenne (genitive plural)
toruksienne (genitive plural)
torustanne (partitive singular)
toruksianne (partitive plural)
toruksessanne (inessive singular)
toruksissanne (inessive plural)
toruksestanne (elative singular)
toruksistanne (elative plural)
torukseenne (illative singular)
toruksiinne (illative plural)
toruksellanne (adessive singular)
toruksillanne (adessive plural)
torukseltanne (ablative singular)
toruksiltanne (ablative plural)
toruksellenne (allative singular)
toruksillenne (allative plural)
toruksenanne (essive singular)
toruksinanne (essive plural)
torukseksenne (singular translative)
toruksiksenne (plural translative)
toruksettanne (abessive singular)
toruksittanne (abessive plural)
toruksinenne (comitative plural)
toruksensa (nominative singular)
toruksensa (nominative plural)
toruksensa (accusative nominative singular)
toruksensa (accusative nominative plural)
toruksensa (accusative genitive singular)
toruksensa (accusative genitive plural)
toruksensa (genitive singular)
torustensa (genitive plural)
toruksiensa (genitive plural)
torustaan (partitive singular)
torustansa (partitive singular)
toruksiaan (partitive plural)
toruksiansa (partitive plural)
toruksessaan (inessive singular)
toruksessansa (inessive singular)
toruksissaan (inessive plural)
toruksissansa (inessive plural)
toruksestaan (elative singular)
toruksestansa (elative singular)
toruksistaan (elative plural)
toruksistansa (elative plural)
torukseensa (illative singular)
toruksiinsa (illative plural)
toruksellaan (adessive singular)
toruksellansa (adessive singular)
toruksillaan (adessive plural)
toruksillansa (adessive plural)
torukseltaan (ablative singular)
torukseltansa (ablative singular)
toruksiltaan (ablative plural)
toruksiltansa (ablative plural)
torukselleen (allative singular)
toruksellensa (allative singular)
toruksilleen (allative plural)
toruksillensa (allative plural)
toruksenaan (essive singular)
toruksenansa (essive singular)
toruksinaan (essive plural)
toruksinansa (essive plural)
toruksekseen (singular translative)
torukseksensa (singular translative)
toruksikseen (plural translative)
toruksiksensa (plural translative)
toruksettaan (abessive singular)
toruksettansa (abessive singular)
toruksittaan (abessive plural)
toruksittansa (abessive plural)
toruksineen (comitative plural)
toruksinensa (comitative plural)


torus

torus (indefinite nominative singular)
torus (genitive indefinite singular)
torusen (definite nominative singular)
torusens (definite genitive singular)
torusar (indefinite nominative plural)
torusars (genitive indefinite plural)
torusarna (definite nominative plural)
torusarnas (definite genitive plural)

(geometry, topology) torus; a shape consisting of a ring, or an object of the same topology residing in a space of higher dimension; especially considered as a Cartesian product of two circles in a four-dimensional space


atlas

Borrowed from Latin Atlas, from the name of the Ancient Greek mythological figure Ἄτλας (Átlas, “Bearer (of the Heavens)”), from τλῆναι (tlênai, “to suffer”, “to endure”, “to bear”). The sense referring to books of maps comes from the Atlas of Mercator, which he named thus in honor of Atlas, who was supposed to be skillful in astronomy and the doctrine of the sphere. The sense referring to the vertebra reflects that the spine carries the globe of the cranium (the neck carries the head).

differential geometry
differential geometry

(differential geometry, topology) A family of coordinate charts that cover a manifold.

atlas

(differential geometry, topology) family of coordinate maps that cover a manifold


proper

en-adj

proper (comparative more proper, superlative most proper)

more proper (comparative)
most proper (superlative)
propa (alternative Geordie)
propre (alternative obsolete)

From Middle English propre, from Anglo-Norman proper, propre, Old French propre (French: propre), from Latin proprius.

luonnonvärinen

heraldry: having its natural or usual coloration

(topology, of a function) Such that the preimage of every compact set is compact.

(topology, of a function) Continuous, mapping closed sets to closed sets, and such that the preimage of every point is compact.


local

local (comparative more local, superlative most local)

more local (comparative)
most local (superlative)

From Middle English local, from Late Latin locālis (“belonging to a place”), possibly also via Old French local; ultimately from Latin locus (“a place”).
The ring-theoretic senses derive from Krull, who first referred to Noetherian commutative rings with a unique maximal ideal as "Stellenring" (Stellen (“place”) + ring) in 1938. The term was inspired by algebraic geometry, where local rings encode information about the behavior of curves (surfaces, etc.) at points; hence, describe "local" behavior.

der

A Hausdorff space satisfying local compactness need not be (globally) compact!

(mathematics, not comparable, of a condition or property) Applying to or satisfied by substructures understood as "near points;" in particular:

(topology) Satisfied by at least one open neighborhood of every point.

(topology) Satisfied by arbitrarily small open neighborhoods of every point.


rand

nl-noun

rand m (plural randen, diminutive randje n)

randen (plural)
randje (diminutive neuter)

Afrikaans: rand

→ Papiamentu: rant

From Middle Dutch rant, from Old Dutch *rant, from Proto-Germanic *randaz.


lattice

→ Japanese: ラティス (ratisu)

From Middle English latis, from Middle French lattis (“lathing”), from Old French lattis, from latte (“a lath”), from Frankish *lattā, *lattu (“a lath”), from Proto-Germanic *lattǭ, *lattō, *laþþō (“board; plank; ledge”), from Proto-Indo-European *(s)latn-, *(s)lat- (“beam; log”). Cognate with Old High German latta (“lath”), (German Latte), Old English lætt (“lath”), Middle Low German lāde (“plank, counter, sales counter”), German Laden (“shop”). More at lath.

cog

(mathematics, algebra) In any of several technical senses, a substructure with properties analogous to those the set of points with integer coordinates bears in relation to the full Euclidian space these points are contained in.

(topology, Lie theory, generalizing sense 5.1) A discrete subgroup L of a given locally compact group G whose quotient space G/L has finite invariant measure.

Lie theory; generalizing sense 5.1; Lie theory; generalizing sense 5.1


angelic

en-adj

angelic (comparative more angelic, superlative most angelic)

more angelic (comparative)
most angelic (superlative)
angelick (alternative)

/ænˈd͡ʒɛlɪk/

From Middle English angelik, aungillik, aungellike, (also angellich, aungellich > English angelly), from Old English anġelīċ, engellīċ, englelīċ, coalescing with Old French angélique, from Latin angelicus, from Ancient Greek ἀγγελικός (angelikós, “of or for a messenger”), from ἄγγελος (ángelos, “angel”). Equivalent to angel + -ic. Doublet of angelique (“plant of the genus Angelica”) and angélique (“plucked bowl lute”).

doublet

(topology) A regular Hausdorff space is said to be angelic if the closure of each relatively countably compact set A is compact and the closure consists of the limits of sequences in A.


orbifold

/ˈɔː.bɪˌfəʊld/

Blend of orbit + manifold. Named by William Thurston.

(topology) A topological space in which every small enough neighborhood is homeomorphic to a quotient of real space by the action of a finite group.


chessboard

chessboards (plural)
chess board (alternative)

(topology) A mathematical construction based on this pattern of squares


Σ

(topology) suspension or reduced suspension


simplex

en-noun

simplex (plural simplexes or (algebraic topology, geometry, linguistics) simplices or simplicia)

simplexes (plural)
simplices (plural)
simplicia (plural)

LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-simplex.wav

LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-simplices.wav

LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-simplicia.wav

Henri Poincaré
MacTutor History of Mathematics Archive
Pieter Hendrik Schoute

The adjective is a learned borrowing from Latin simplex (“plain, simple; single”). The first part, sim-, comes from Proto-Indo-European *sem-, *sm̥- (“one; together”). The second part, -plex, may be from *pleḱ- (“to weave”).
The noun is derived from the adjective. The plural forms simplices and simplicia are learned borrowings from Latin simplicēs (masculine or feminine) and simplicia (neuter), respectively plural forms of simplex.
Noun sense 1 (“generalization of a triangle or tetrahedron to an arbitrary dimension”) was apparently coined by the Dutch mathematician Pieter Hendrik Schoute (1846–1913) as a short version of Simplicissimum in Mehrdimensionale Geometrie (in German, 1902). (In his pioneering works on algebraic topology, the French mathematician Henri Poincaré (1854–1912) had previously introduced the concept, but not the actual term simplex.)

lbor

affinely independent
affinely independent

(algebraic topology, geometry) A generalization of a triangle or tetrahedron to an arbitrary dimension, the generalization being the simplest possible convex polytope for a given dimension; more accurately, the convex hull of n+1 affinely independent points in n-dimensional space.


chart

→ Japanese: チャート (chāto)

→ Korean: 차트 (chateu)

→ Swahili: chati

→ Welsh: siart

Borrowed from Middle French charte (“card, map”), from Late Latin charta (“paper, card, map”), Latin charta (“papyrus, writing”), from Ancient Greek χάρτης (khártēs, “papyrus, thin sheet”). See charter, card, carte.

der

coordinate chart
coordinate chart#English

(differential geometry, topology) Synonym of coordinate chart.


kula

kulka (diminutive)
kula (nominative singular)
kule (nominative plural)
kuli (genitive singular)
kul (genitive plural)
kuli (genitive plural)
kuli (dative singular)
kulom (dative plural)
kulę (accusative singular)
kule (accusative plural)
kulą (instrumental singular)
kulami (instrumental plural)
kuli (locative singular)
kulach (locative plural)
kulo (singular vocative)
kule (plural vocative)

→ Belarusian: ку́ля (kúlja)

desc

→ Russian: пу́ля (púlja) (with sound changes)

→ Ukrainian: ку́ля (kúlja)

Apparently borrowed from Middle High German kūle. In most senses cognate with German Kugel, in the sense “crutch” cognate with German Keule.


section

From Middle English seccioun, from Old French section, from Latin sectiō (“cutting, cutting off, excision, amputation of diseased parts of the body, etc.”), from sectus, past participle of secāre (“to cut”). More at saw.

разрэ́з

surgery: incision or the act of making an incision

A cross-section (image that shows an object as if cut along a plane).

(topology) A function that generalizes the notion of the graph of a function; formally, a continuous right inverse to the projection map of a fiber bundle.


boundary

From bound + -ary, Old French, from Latin.

(topology) (of a set) the set of points in the closure of a set S, not belonging to the interior of that set

邊界 /边界

(topology) the set of points in the closure, not belonging to the interior


normal

en-adj

normal (comparative normaler or more normal, superlative normalest or most normal)

normaler (comparative)
more normal (comparative)
normalest (superlative)
most normal (superlative)

From Latin normālis (“made according to a carpenter's square; later: according to a rule”), from nōrma (“carpenter's square”), of uncertain origin; doublet of normale. The earliest meaning of the word in English was "perpendicular; forming a right angle" like something normālis (“made according to a carpenter's square”), but by Late Latin normālis had also come to mean "according to a rule", from which modern English senses of the word derive: in the 1800s, as people began to quantitatively study things like height, weight and blood pressure, the usual or most common values came to be called "normal", and by extension values regarded as healthy or desirable came to be called "normal" regardless of their usuality.

der

According to norms or rules or to a regular pattern.

(mathematics) Adhering to or being what is considered natural or regular in a particular field or context:

(topology, of a topology or topological space) In which disjoint closed sets can be separated by disjoint neighborhoods.


neighborhood

en-noun

neighborhood (countable and uncountable, plural neighborhoods)

neighborhoods (plural)
neighbourhood (alternative UK)

From an alteration of earlier neighborred (“neighborhood”), from Middle English neȝeburredde, neheborreden, equivalent to neighbor + -red; the term being interpreted as neighbor + -hood. For change in suffix (-red to -hood), compare brotherhood.
Cognates
Dutch nabijheid (common in modern language), Dutch naburigheid (uncommon in modern language).

veïnat

topology: set containing an open set which contains some specified point

vizinhança

topology: set containing an open ball which contains a specified point

A set containing an open set which contains some specified point.

Alternatively: An open set which contains some specified point.

A set containing an open ball which contains a specified point.

Alternatively: An open ball which contains some specified point.

(topology) The infinitesimal open set of all points that may be reached directly from a given point.

lähiympäristö

topology: set of all points that may be reached directly from a given point


domination

domination (countable and uncountable, plural dominations)

/ˌdɒməˈneɪʃən/

/ˌdɑːməˈneɪʃən/

From Middle English domynacion, from Old French dominacion, from Latin dominātiō (“rule, dominion”), from dominor (“domineer; rule”); see dominate.

With more than 200 research papers published on the algorithmic complexity of domination and related parameters of graphs, it is difficult to know what to cover in a relatively short chapter on the subject, especially since it could take quite a few pages just to cover the preliminaries of computational complexity and the many algorithm design paradigms that have been applied to domination problems.

1998, Teresa W. Haynes, Stephen T. Hedetniemi, Peter J. Slater, Fundamentals of Domination in Graphs, →ISBN, page 299:


foliation

foliation (countable and uncountable, plural foliations)

/fəʊlɪˈeɪʃn/

From French foliation, from Latin folium (“leaf”).

Historically, the formalism which first arose for the material we discuss is that of measured foliations in surfaces.

1992, R. C. Penner, Combinatorics of Train Tracks, page 204:

We will show that every closed 3-manifold has a foliation of codimension one. In 1952, G. Reeb published his construction of a foliation of the 3-sphere. About twelve years later, W. Lickorish [123] exhibited foliations of codimension one on every closed, orientable 3-manifold.

2003, Alberto Candel, Lawrence Conlon, Foliations, Vol.2, p.253

The simplest example of a foliation is provided by a single submersion F : M → N, M and N being manifolds.

2004, Paweł Grzegorz Walczak, Dynamics Of Foliations, Groups And Pseudogroups, Monografie Matematyczne: Vol.64, New Series, p.6

(topology) A set of submanifolds of a given manifold, each of which is of lower dimension than it, but which, taken together, are coextensive with it.

叶层结构

topology: a set of subspaces coextensive with a manifold


shell

en-verb

shell (third-person singular simple present shells, present participle shelling, simple past and past participle shelled)

shells (present singular third-person)
shelling (participle present)
shelled (participle past)
shelled (past)

From Middle English schelle, from Old English sċiell, from Proto-West Germanic *skallju, from Proto-Germanic *skaljō, from Proto-Indo-European *(s)kelH- (“to split, cleave”).
Compare West Frisian skyl (“peel, rind”), Dutch schil (“peel, skin, rink”), Low German Schell (“shell, scale”), Irish scelec (“pebble”), Old Church Slavonic сколика (skolika, “shell”). More at shale.
Doublet of sheal.
* (computing): From being viewed as an outer layer of interface between the user and the operating-system internals.


collection

en-noun

collection (countable and uncountable, plural collections)

From Middle English colleccioun, collection, from Old French collection, from Latin collēctiō, collēctiōnem, from collēctus, from colligō (“collect together”), composed of con- + legō (“bring together, gather, collect”), ultimately from Proto-Indo-European *leǵ- (“to gather, collect”).

der

(set theory, topology, mathematical analysis) A set of sets; used because such a thing is in general too large to comply with the formal definition of a set.


dense

en-adj

dense (comparative denser, superlative densest)

denser (comparative)
densest (superlative)

From Middle French dense, from Latin dēnsus, from Proto-Indo-European *dens- (“thick, dense”) (whence also Ancient Greek δασύς (dasús)).

der

(mathematics, topology, of a subset S of a topological space T, not comparable) Such that its closure in T is T.


cone

From Middle English cone (“corner, angle”) and conoun (“cone”), from Medieval Latin cōnus, cōnon (“cone, wedge, peak”), from Ancient Greek κῶνος (kônos, “cone, spinning top, pine cone”). Reinforced by Middle French cone, from the same Graeco-Latin source.

(topology) A space formed by taking the direct product of a given space with a closed interval and identifying all of one end to a point.


excision

en-noun

excision (countable and uncountable, plural excisions)

From Middle French excision, from Latin excīsiō.

(topology) The fact that, under certain hypotheses, the homology of a space relative to a subspace is unchanged by the identification of a subspace of the latter to a point.


coherent

en-adj

coherent (comparative more coherent, superlative most coherent)

more coherent (comparative)
most coherent (superlative)
cohærent (alternative)

/kəʊˈhɪə.ɹənt/

/kəʉˈhɪə.ɹənt/

From Middle French coherent, from Latin cohaērēns, from co- + haereō. By surface analysis, cohere + -ent.

(topology, of a topology 𝒯 on a set T with respect to a family C_a of subsets of T) In a technical sense, determined by the (topology of) the subsets. Formally, Such that 𝒯 is the finest topology on T for which the inclusion maps ιₐ:C_a→T are continuous, where each C_a is considered with its subspace topology.


vector space

LL-Q1860 (eng)-Flame, not lame-vector space.wav

A vector space is a set of vectors which can be linearly combined.

Each vector space has a basis and dimension.

scalar multiplication
scalar multiplication

(algebra, geometry, topology) A set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints; equivalently, a module over a field.


compact

compact (comparative more compact or compacter, superlative most compact or compactest)

more compact (comparative)
compacter (comparative)
most compact (superlative)
compactest (superlative)

From Middle French compact, from Latin compāctus, perfect passive participle of compingō (“join together”), from com- (“together”) + pangō (“fasten”), from Proto-Indo-European *pag- (“to fasten”).

massive compact halo object

massive and compact halo object, massive astronomical compact halo object, massive astrophysical compact halo object

sequentially compact
sequentially compact

(topology, not comparable) Of a topological space:

Such that every open cover has a finite subcover. In a metric space, this is equivalent to being sequentially compact. In metric spaces with the Heine-Borel property, this is equivalent to being closed and bounded.

Compact in the above sense and moreover Hausdorff.


clopen

A subset of a metric space is clopen iff it is both closed and open. A metric space is called zero-dimensional iff there is a base for the open sets consisting of clopen sets.

1990, Gerald A Edgar, Measure, Topology, and Fractal Geometry, page 80:

1999, S. J. Dilworth, On the extensibility of certain homeomorphisms and linear isometries, Krzysztof Jarosz (editor), Function Spaces: Proceedings of the Third Conference on Function Spaces, American Mathematical Society, Contemporary Mathematics, Volume 232, page 124,
FACT 1. Disjoint closed subsets of ℕN may be separated by disjoint clopen sets.

Theorem 3. 1) Every two disjoint closed sets in a totally disconnected compact space #92;mathfrak#123;Q#125; are separated by disjoint clopen sets.
2) Every algebra of clopen sets which separates the points of a totally disconnected compact space contains all clopen sets.

2002, D. A. Vladimirov, Boolean Algebras in Analysis, page 133:

(topology, of a set in a topological space) Both open and closed.


kartta

kartta (nominative singular)
kartat (nominative plural)
kartta (accusative nominative singular)
kartat (accusative nominative plural)
kartan (accusative genitive singular)
kartat (accusative genitive plural)
kartan (genitive singular)
karttojen (genitive plural)
karttain (genitive plural rare)
karttaa (partitive singular)
karttoja (partitive plural)
kartassa (inessive singular)
kartoissa (inessive plural)
kartasta (elative singular)
kartoista (elative plural)
karttaan (illative singular)
karttoihin (illative plural)
kartalla (adessive singular)
kartoilla (adessive plural)
kartalta (ablative singular)
kartoilta (ablative plural)
kartalle (allative singular)
kartoille (allative plural)
karttana (essive singular)
karttoina (essive plural)
kartaksi (singular translative)
kartoiksi (plural translative)
kartatta (abessive singular)
kartoitta (abessive plural)
kartoin (instructive plural)
See the possessive forms below. (comitative)
karttani (nominative singular)
karttani (nominative plural)
karttani (accusative nominative singular)
karttani (accusative nominative plural)
karttani (accusative genitive singular)
karttani (accusative genitive plural)
karttani (genitive singular)
karttojeni (genitive plural)
karttaini (genitive plural rare)
karttaani (partitive singular)
karttojani (partitive plural)
kartassani (inessive singular)
kartoissani (inessive plural)
kartastani (elative singular)
kartoistani (elative plural)
karttaani (illative singular)
karttoihini (illative plural)
kartallani (adessive singular)
kartoillani (adessive plural)
kartaltani (ablative singular)
kartoiltani (ablative plural)
kartalleni (allative singular)
kartoilleni (allative plural)
karttanani (essive singular)
karttoinani (essive plural)
kartakseni (singular translative)
kartoikseni (plural translative)
kartattani (abessive singular)
kartoittani (abessive plural)
karttoineni (comitative plural)
karttasi (nominative singular)
karttasi (nominative plural)
karttasi (accusative nominative singular)
karttasi (accusative nominative plural)
karttasi (accusative genitive singular)
karttasi (accusative genitive plural)
karttasi (genitive singular)
karttojesi (genitive plural)
karttaisi (genitive plural rare)
karttaasi (partitive singular)
karttojasi (partitive plural)
kartassasi (inessive singular)
kartoissasi (inessive plural)
kartastasi (elative singular)
kartoistasi (elative plural)
karttaasi (illative singular)
karttoihisi (illative plural)
kartallasi (adessive singular)
kartoillasi (adessive plural)
kartaltasi (ablative singular)
kartoiltasi (ablative plural)
kartallesi (allative singular)
kartoillesi (allative plural)
karttanasi (essive singular)
karttoinasi (essive plural)
kartaksesi (singular translative)
kartoiksesi (plural translative)
kartattasi (abessive singular)
kartoittasi (abessive plural)
karttoinesi (comitative plural)
karttamme (nominative singular)
karttamme (nominative plural)
karttamme (accusative nominative singular)
karttamme (accusative nominative plural)
karttamme (accusative genitive singular)
karttamme (accusative genitive plural)
karttamme (genitive singular)
karttojemme (genitive plural)
karttaimme (genitive plural rare)
karttaamme (partitive singular)
karttojamme (partitive plural)
kartassamme (inessive singular)
kartoissamme (inessive plural)
kartastamme (elative singular)
kartoistamme (elative plural)
karttaamme (illative singular)
karttoihimme (illative plural)
kartallamme (adessive singular)
kartoillamme (adessive plural)
kartaltamme (ablative singular)
kartoiltamme (ablative plural)
kartallemme (allative singular)
kartoillemme (allative plural)
karttanamme (essive singular)
karttoinamme (essive plural)
kartaksemme (singular translative)
kartoiksemme (plural translative)
kartattamme (abessive singular)
kartoittamme (abessive plural)
karttoinemme (comitative plural)
karttanne (nominative singular)
karttanne (nominative plural)
karttanne (accusative nominative singular)
karttanne (accusative nominative plural)
karttanne (accusative genitive singular)
karttanne (accusative genitive plural)
karttanne (genitive singular)
karttojenne (genitive plural)
karttainne (genitive plural rare)
karttaanne (partitive singular)
karttojanne (partitive plural)
kartassanne (inessive singular)
kartoissanne (inessive plural)
kartastanne (elative singular)
kartoistanne (elative plural)
karttaanne (illative singular)
karttoihinne (illative plural)
kartallanne (adessive singular)
kartoillanne (adessive plural)
kartaltanne (ablative singular)
kartoiltanne (ablative plural)
kartallenne (allative singular)
kartoillenne (allative plural)
karttananne (essive singular)
karttoinanne (essive plural)
kartaksenne (singular translative)
kartoiksenne (plural translative)
kartattanne (abessive singular)
kartoittanne (abessive plural)
karttoinenne (comitative plural)
karttansa (nominative singular)
karttansa (nominative plural)
karttansa (accusative nominative singular)
karttansa (accusative nominative plural)
karttansa (accusative genitive singular)
karttansa (accusative genitive plural)
karttansa (genitive singular)
karttojensa (genitive plural)
karttainsa (genitive plural rare)
karttaansa (partitive singular)
karttojaan (partitive plural)
karttojansa (partitive plural)
kartassaan (inessive singular)
kartassansa (inessive singular)
kartoissaan (inessive plural)
kartoissansa (inessive plural)
kartastaan (elative singular)
kartastansa (elative singular)
kartoistaan (elative plural)
kartoistansa (elative plural)
karttaansa (illative singular)
karttoihinsa (illative plural)
kartallaan (adessive singular)
kartallansa (adessive singular)
kartoillaan (adessive plural)
kartoillansa (adessive plural)
kartaltaan (ablative singular)
kartaltansa (ablative singular)
kartoiltaan (ablative plural)
kartoiltansa (ablative plural)
kartalleen (allative singular)
kartallensa (allative singular)
kartoilleen (allative plural)
kartoillensa (allative plural)
karttanaan (essive singular)
karttanansa (essive singular)
karttoinaan (essive plural)
karttoinansa (essive plural)
kartakseen (singular translative)
kartaksensa (singular translative)
kartoikseen (plural translative)
kartoiksensa (plural translative)
kartattaan (abessive singular)
kartattansa (abessive singular)
kartoittaan (abessive plural)
kartoittansa (abessive plural)
karttoineen (comitative plural)
karttoinensa (comitative plural)

→ Northern Sami: gárta

Borrowed from Swedish karta, ultimately from Latin charta, from Ancient Greek χάρτης (khártēs).

[ˈkɑ̝rt̪ːɑ̝]

(differential geometry, topology) coordinate chart


isotope

en-verb

isotope (third-person singular simple present isotopes, present participle isotoping, simple past and past participle isotoped)

isotopes (present singular third-person)
isotoping (participle present)
isotoped (participle past)
isotoped (past)

(topology, transitive) To define or demonstrate an isotopy of (one map with another).


surgery

en-noun

surgery (countable and uncountable, plural surgeries)

/ˈsɜːd͡ʒəɹi/

From Middle English surgerie, from Old French surgerie, from Latin chirurgia, from Ancient Greek χειρουργία (kheirourgía), from χείρ (kheír, “hand”) + ἔργον (érgon, “work”). Doublet of chirurgy.

(topology) The production of a manifold by removing parts of one manifold and replacing them with corresponding parts of others.


descent

descent (countable and uncountable, plural descents)

From Middle English and Anglo-Norman descente, from Anglo-Norman descendre (“to descend”); see descend. Compare ascent, ascend. Doublet of desant.

(topology) A particular extension of the idea of gluing.


covering

covering (countable and uncountable, plural coverings)

From Middle English coverynge, -inge, keverynge, -inge [verbal noun of coveren, keveren (“to cover”)]; or, verbal noun from cover (verb) + -ing.

(topology, of a given open set U) A collection of sets U_i such that their union contains U; such a collection with the additional property that every U_i is open; such a collection with the additional property that every U_i is contained in U.

(topology) A special kind of map that establishes a relationship between two topological spaces in the sense that, under the action of the map, the one looks locally like several copies of the second: Formally, a continuous map π:E→X between topological spaces such that there exists, for every point x in X, a discrete space D_x and an open neighborhood U of x such that π⁻¹(U)= displaystyle ⨆_(d∈D_x)V_d and π|_(V_d):V_d→U is a homeomorphism for every d∈D_x. See Covering space on Wikipedia.Wikipedia


Möbius strip

Möbius strips (plural)
Mobius strip (alternative)
Moebius strip (alternative)

August Ferdinand Möbius
Johann Benedict Listing
Möbius strip

Named after August Ferdinand Möbius (1790–1868), one of two German mathematicians—the other being Johann Benedict Listing (1808–1882)—who independently discovered the strip at the same time (1858).

Like a mind moving on a Möbius strip of events, one's consciousness goes over the same territory again and again without ever becoming aware of the nature of awareness.

1981, William Irwin Thompson, The Time Falling Bodies Take to Light: Mythology, Sexuality and the Origins of Culture, page 8:

1991, Theoni Pappas, More Joy of Mathematics, Wide World Publishing, page 117,
B. F. Goodrich Co. has a patent for a Möbius strip conveyor belt. It lasts longer since the wear and tear is spread uniformly over the entire surface.

A geometrical model of electron (positron) structure is presented based upon an object of two linked loops obtained by cutting a Möbius strip asymmetrically.

1992, Speculations in Science and Technology, Volume 15, Elsevier Sequoia, page 221:

Proust's novel grew and deepened into over 3,000 pages of everything and nothing: a Möbius strip of profundity twisting into mundanity, mundanity twisting into profundity.

2013 November 16, Patrick McGuinness, “Who's afraid of Marcel Proust?”, in The Daily Telegraph (Review), page R20:

(topology) A one-sided surface formed by identifying two opposite edges of a square in opposite senses;

A one-sided surface formed by identifying two opposite edges of a square in opposite senses;
a narrow strip given a half twist and joined at the ends, forming a three-dimensional embedding of said surface.


orientation

orientation (countable and uncountable, plural orientations)

→ Japanese: オリエンテーション (orientēshon)

→ Korean: 오리엔테이션 (orienteisyeon)

/ˌɔɹiɛnˈteɪʃən/

From French orientation. By surface analysis, orient + -ation.

(analytic geometry, topology, countable) The designation of a parametrised curve as "positively" or "negatively" oriented; the analogous description of a surface or hypersurface.


virtually

en-adv

virtually (comparative more virtually, superlative most virtually)

more virtually (comparative)
most virtually (superlative)

/ˈvɜːt͡ʃʊəli/

/ˈvɜːt͡ʃəli/

/ˈvɜːt͡ʃʉəli/

/ˈvɵːt͡ʃʉəli/

/ˈvɵːt͡ʃəli/

From Middle English vertually; equivalent to virtual + -ly.

Another class of small manifolds consists of those that are not virtually Haken (a manifold is virtually Haken if it is finitely covered by a Haken manifold).

2002, Steven Boyer, “Dehn surgery on knots” (chapter 4), in R.J. Daverman, R.B. Sher, editors, Handbook of Geometric Topology, page 206:

We call a hyperplane Y in a VH-complex X virtually clean if there exists a finite-sheeted covering map p : X̂ → X and a connected component Y ⊆ p⁻¹Y such that the hyperplane Ŷ of X̂ is clean.

2017, Martin R. Bridson, Henry Wilton, “Hyperbolic Geometry and Geometric Group Theory”, in Advanced Studies in Pure Mathematics, volume 73, page 40:

(topology) Of a covering space of finite degree.


saturated

en-adj

saturated (comparative more saturated, superlative most saturated)

more saturated (comparative)
most saturated (superlative)

LL-Q1860 (eng)-Flame, not lame-saturated.wav

equivalence relation
equivalence relation

(mathematics, set theory, of a set S, with respect to an equivalence relation ≡) Equal to a union of equivalence classes of ≡; such that if x∈S and x≡y then y∈S.

(mathematics, especially topology, with respect to a function f) Saturated with respect to the equivalence relation x≡y⟺f(x)=f(y) (the kernel, sense 10, of f).


loop

From Middle English loupe (“noose, loop”), earlier lowp-knot (“loop-knot”), of North Germanic origin, from Old Norse hlaup (“a run”), used in the sense of a "running knot", from hlaupa (“to leap”), ultimately from Proto-Germanic *hlaupaną (“to leap, run”). Compare Swedish löp-knut (“loop-knot”), Danish løb-knude (“a running knot”), Danish løb (“a course”). More at leap. The verb is derived from the noun.

der

(topology) A path that starts and ends at the same point.

silmukka

topology: path that starts and ends at the same point


α

alpha

for names of this symbol in other language


companion

From Middle English companion, from Old French compaignon (“companion”) (modern French compagnon), from Late Latin compāniōn- (nominative singular compāniō, whence French copain), from com- + pānis (literally, with + bread), a word first attested in the Frankish Lex Salica as a calque of a Germanic word, probably Frankish *galaibo, *gahlaibō (“messmate”, literally “with-bread”), from Proto-Germanic *gahlaibô. Compare also Old High German galeipo (“messmate”) and Gothic 𐌲𐌰𐌷𐌻𐌰𐌹𐌱𐌰 (gahlaiba, “messmate”); and, for the semantics, compare Old Armenian ընկեր (ənker, “friend”, literally “messmate”). More at co-, loaf. Displaced native Old English ġefēra (literally “fellow traveler”). Doublet of company. Compare mate.

noncog

(topology) A knot in whose neighborhood another, specified knot meets every meridian disk.


subcover

The open intervals cover the real numbers; the open intervals of the form (x, x+1) are a subcover.

(topology) A cover which is a subset of another cover.


I

From the Etruscan letter 𐌉 (i), from the Ancient Greek letter Ι (I, iota), derived from the Phoenician letter 𐤉 (y, yod), from the Egyptian hieroglyph 𓂝.

(mathematical analysis, topology) the (closed) unit interval; [0, 1]


S

From the Etruscan letter 𐌔 (s, “es”), from the Ancient Greek letter Σ (S, “sigma”), derived from the Phoenician letter 𐤔 (š, “šin”), from the Egyptian hieroglyph 𓌒.


PL

piecewise linear
piecewise linear#English

(topology) Initialism of piecewise linear.


suku

suku (nominative singular)
suvut (nominative plural)
suku (accusative nominative singular)
suvut (accusative nominative plural)
suvun (accusative genitive singular)
suvut (accusative genitive plural)
suvun (genitive singular)
sukujen (genitive plural)
sukua (partitive singular)
sukuja (partitive plural)
suvussa (inessive singular)
suvuissa (inessive plural)
suvusta (elative singular)
suvuista (elative plural)
sukuun (illative singular)
sukuihin (illative plural)
suvulla (adessive singular)
suvuilla (adessive plural)
suvulta (ablative singular)
suvuilta (ablative plural)
suvulle (allative singular)
suvuille (allative plural)
sukuna (essive singular)
sukuina (essive plural)
suvuksi (singular translative)
suvuiksi (plural translative)
suvutta (abessive singular)
suvuitta (abessive plural)
suvuin (instructive plural)
See the possessive forms below. (comitative)
sukuni (nominative singular)
sukuni (nominative plural)
sukuni (accusative nominative singular)
sukuni (accusative nominative plural)
sukuni (accusative genitive singular)
sukuni (accusative genitive plural)
sukuni (genitive singular)
sukujeni (genitive plural)
sukuani (partitive singular)
sukujani (partitive plural)
suvussani (inessive singular)
suvuissani (inessive plural)
suvustani (elative singular)
suvuistani (elative plural)
sukuuni (illative singular)
sukuihini (illative plural)
suvullani (adessive singular)
suvuillani (adessive plural)
suvultani (ablative singular)
suvuiltani (ablative plural)
suvulleni (allative singular)
suvuilleni (allative plural)
sukunani (essive singular)
sukuinani (essive plural)
suvukseni (singular translative)
suvuikseni (plural translative)
suvuttani (abessive singular)
suvuittani (abessive plural)
sukuineni (comitative plural)
sukusi (nominative singular)
sukusi (nominative plural)
sukusi (accusative nominative singular)
sukusi (accusative nominative plural)
sukusi (accusative genitive singular)
sukusi (accusative genitive plural)
sukusi (genitive singular)
sukujesi (genitive plural)
sukuasi (partitive singular)
sukujasi (partitive plural)
suvussasi (inessive singular)
suvuissasi (inessive plural)
suvustasi (elative singular)
suvuistasi (elative plural)
sukuusi (illative singular)
sukuihisi (illative plural)
suvullasi (adessive singular)
suvuillasi (adessive plural)
suvultasi (ablative singular)
suvuiltasi (ablative plural)
suvullesi (allative singular)
suvuillesi (allative plural)
sukunasi (essive singular)
sukuinasi (essive plural)
suvuksesi (singular translative)
suvuiksesi (plural translative)
suvuttasi (abessive singular)
suvuittasi (abessive plural)
sukuinesi (comitative plural)
sukumme (nominative singular)
sukumme (nominative plural)
sukumme (accusative nominative singular)
sukumme (accusative nominative plural)
sukumme (accusative genitive singular)
sukumme (accusative genitive plural)
sukumme (genitive singular)
sukujemme (genitive plural)
sukuamme (partitive singular)
sukujamme (partitive plural)
suvussamme (inessive singular)
suvuissamme (inessive plural)
suvustamme (elative singular)
suvuistamme (elative plural)
sukuumme (illative singular)
sukuihimme (illative plural)
suvullamme (adessive singular)
suvuillamme (adessive plural)
suvultamme (ablative singular)
suvuiltamme (ablative plural)
suvullemme (allative singular)
suvuillemme (allative plural)
sukunamme (essive singular)
sukuinamme (essive plural)
suvuksemme (singular translative)
suvuiksemme (plural translative)
suvuttamme (abessive singular)
suvuittamme (abessive plural)
sukuinemme (comitative plural)
sukunne (nominative singular)
sukunne (nominative plural)
sukunne (accusative nominative singular)
sukunne (accusative nominative plural)
sukunne (accusative genitive singular)
sukunne (accusative genitive plural)
sukunne (genitive singular)
sukujenne (genitive plural)
sukuanne (partitive singular)
sukujanne (partitive plural)
suvussanne (inessive singular)
suvuissanne (inessive plural)
suvustanne (elative singular)
suvuistanne (elative plural)
sukuunne (illative singular)
sukuihinne (illative plural)
suvullanne (adessive singular)
suvuillanne (adessive plural)
suvultanne (ablative singular)
suvuiltanne (ablative plural)
suvullenne (allative singular)
suvuillenne (allative plural)
sukunanne (essive singular)
sukuinanne (essive plural)
suvuksenne (singular translative)
suvuiksenne (plural translative)
suvuttanne (abessive singular)
suvuittanne (abessive plural)
sukuinenne (comitative plural)
sukunsa (nominative singular)
sukunsa (nominative plural)
sukunsa (accusative nominative singular)
sukunsa (accusative nominative plural)
sukunsa (accusative genitive singular)
sukunsa (accusative genitive plural)
sukunsa (genitive singular)
sukujensa (genitive plural)
sukuaan (partitive singular)
sukuansa (partitive singular)
sukujaan (partitive plural)
sukujansa (partitive plural)
suvussaan (inessive singular)
suvussansa (inessive singular)
suvuissaan (inessive plural)
suvuissansa (inessive plural)
suvustaan (elative singular)
suvustansa (elative singular)
suvuistaan (elative plural)
suvuistansa (elative plural)
sukuunsa (illative singular)
sukuihinsa (illative plural)
suvullaan (adessive singular)
suvullansa (adessive singular)
suvuillaan (adessive plural)
suvuillansa (adessive plural)
suvultaan (ablative singular)
suvultansa (ablative singular)
suvuiltaan (ablative plural)
suvuiltansa (ablative plural)
suvulleen (allative singular)
suvullensa (allative singular)
suvuilleen (allative plural)
suvuillensa (allative plural)
sukunaan (essive singular)
sukunansa (essive singular)
sukuinaan (essive plural)
sukuinansa (essive plural)
suvukseen (singular translative)
suvuksensa (singular translative)
suvuikseen (plural translative)
suvuiksensa (plural translative)
suvuttaan (abessive singular)
suvuttansa (abessive singular)
suvuittaan (abessive plural)
suvuittansa (abessive plural)
sukuineen (comitative plural)
sukuinensa (comitative plural)


annulus

Learned borrowing from Medieval Latin ānnulus, a misspelling of Latin ānulus (“ring, especially one worn on a finger”), from ānus (“ring”) (from Proto-Indo-European *h₁eh₂no- (“ring”)) + -ulus (diminutive suffix).
The plural form annuli is a learned borrowing from Medieval Latin ānnulī.

lbor

(topology) Any topological space homeomorphic to the region in a plane between two concentric circles of different radii.


embedding

(mathematics) A map which, in any of several technical senses, represents the containment of one structure inside another.

(topology) A continuous map which is also a homeomorphism between its domain and its image (considered with the subspace topology induced by its codomain).


saturation

en-noun

saturation (usually uncountable, plural saturations)

LL-Q1860 (eng)-Flame, not lame-saturation.wav

Etymology tree
Late Latin saturatiobor.
English saturation
Borrowed from Late Latin saturatio, saturationem.

etymon

(mathematics, set theory, topology, of a set S, with respect to an equivalence relation or function, countable) The smallest set containing S which is saturated with respect to the equivalence relation or function.


approximately equal to; congruent to; isomorphic to


topology

en-noun

topology (countable and uncountable, plural topologies)

From Late Latin topologia, from Ancient Greek τόπος (tópos, “place, locality”) + -(o)logy (“study of, a branch of knowledge”).

topologie

study of geometric properties that are not changed by stretching etc.

A set X equipped with a topology #92;tau is called a topological space and denoted (X,#92;tau).

The subsets of a set X which constitute a topology are called the open sets of X.

It is easy to verify that the topology generated by these basic open sets coincides with the definition of the topology on #92;widehat#123;V#125; above, for the Zariski topology and the sheaf of functions #92;operatorname#123;val#125;(f),f regular.

2016, Ehud Hrushovski, François Loeser, Non-Archimedean Tame Topology and Stably Dominated Types (AM-192), Princeton University Press, page 43:

(topology) Any collection τ of subsets of a given set X that contains both the empty set and X, and which is closed under finitary intersections and arbitrary unions.


trefoil

From Middle English trefoil, from Old French trifoil, trefeul, from Latin trifolium, from tri- (“three”) + folium (“leaf”).


β

IPA


pointed

en-adj

pointed (comparative more pointed, superlative most pointed)

more pointed (comparative)
most pointed (superlative)

The class of all pointed spaces forms a category - Top_• - with basepoint preserving continuous maps as morphisms.

(topology, algebraic topology, of a topological space) That has a named, but otherwise arbitrary, point (called the basepoint) that remains unchanged during subsequent discussion and is kept track of during all operations.


connected

connected (comparative more connected, superlative most connected)

more connected (comparative)
most connected (superlative)

As a combinatorial subject, the connected dominating set has been studied in as early as 1970s.

2012, Ding-Zhu Du, Peng-Jun Wan, Connected Dominating Set: Theory and Applications, →ISBN, page v:

(mathematics, topology, of a topological space) That cannot be partitioned into two nonempty open sets.

souvislý

topology: cannot be partitioned into two nonempty open sets


hyperbolic

hyperbolical (alternative)
hyperbolick (alternative)

hyperbolic partial differential equation

A hyperbolic isometry f has two (distinct) fixed points on ∂ℋ.

2001, A. F. Beardon, "The Geometry of Riemann Surfaces", in, E. Bujalance, A. F. Costa, and E. Martínez, editors, Topics on Riemann Surfaces and Fuchsian Groups, Cambridge, page 6 http://books.google.com/books?id=RjbQdcP7DgwC&pg=PA6&dq=hyperbolic

(geometry, topology, of an automorphism) Whose domain has two (possibly ideal) fixed points joined by a line mapped to itself by translation.

Exactly one hypercycle is a hyperbolic geodesic, and this is called the axis A_f of f.

(topology) Of, pertaining to, or in a hyperbolic space (a space having negative curvature or sectional curvature).


Klein bottle

Calque of German Kleinsche Flasche, named after German mathematician Felix Klein (1849–1925), who first described such a surface in 1882.

named-after

At this level Atman and Brahman are like a Klein bottle or a Möbius strip: there is no edge where one can say that this is Atman, but this is Brahman.

1981, William Irwin Thompson, The Time Falling Bodies Take to Light: Mythology, Sexuality and the Origins of Culture, London: Rider/Hutchinson & Co., page 222:

(topology) The closed manifold obtained by identifying the boundary components of the annulus so that the resultant surface is nonorientable.


retract

Partly:
* from retract (verb) (see etymology 1); and
* from Late Latin retractus (“a pulling back, retreat; refuge”), from Latin retractus (“withdrawn”), the perfect passive participle of Latin retrahō (“to draw or pull back, withdraw; to bring back; to compel to turn back; to recall; to get back, recover; to hold back, restrain, withhold; to remove, take away; to bring to light again; (Late Latin) to delay”) (see etymology 1) + -tus (suffix forming action nouns from verbs). Doublet of retrait, retreat, and ritratto.


irreducible

en-adj

irreducible (comparative more irreducible, superlative most irreducible)

more irreducible (comparative)
most irreducible (superlative)

/ˌɪɹɪˈdjuːsɪbəl/

LL-Q1860 (eng)-Flame, not lame-irreducible.wav

(topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.


kanta

kanta (nominative singular)
kannat (nominative plural)
kanta (accusative nominative singular)
kannat (accusative nominative plural)
kannan (accusative genitive singular)
kannat (accusative genitive plural)
kannan (genitive singular)
kantojen (genitive plural)
kantain (genitive plural rare)
kantaa (partitive singular)
kantoja (partitive plural)
kannassa (inessive singular)
kannoissa (inessive plural)
kannasta (elative singular)
kannoista (elative plural)
kantaan (illative singular)
kantoihin (illative plural)
kannalla (adessive singular)
kannoilla (adessive plural)
kannalta (ablative singular)
kannoilta (ablative plural)
kannalle (allative singular)
kannoille (allative plural)
kantana (essive singular)
kantoina (essive plural)
kannaksi (singular translative)
kannoiksi (plural translative)
kannatta (abessive singular)
kannoitta (abessive plural)
kannoin (instructive plural)
See the possessive forms below. (comitative)
kantani (nominative singular)
kantani (nominative plural)
kantani (accusative nominative singular)
kantani (accusative nominative plural)
kantani (accusative genitive singular)
kantani (accusative genitive plural)
kantani (genitive singular)
kantojeni (genitive plural)
kantaini (genitive plural rare)
kantaani (partitive singular)
kantojani (partitive plural)
kannassani (inessive singular)
kannoissani (inessive plural)
kannastani (elative singular)
kannoistani (elative plural)
kantaani (illative singular)
kantoihini (illative plural)
kannallani (adessive singular)
kannoillani (adessive plural)
kannaltani (ablative singular)
kannoiltani (ablative plural)
kannalleni (allative singular)
kannoilleni (allative plural)
kantanani (essive singular)
kantoinani (essive plural)
kannakseni (singular translative)
kannoikseni (plural translative)
kannattani (abessive singular)
kannoittani (abessive plural)
kantoineni (comitative plural)
kantasi (nominative singular)
kantasi (nominative plural)
kantasi (accusative nominative singular)
kantasi (accusative nominative plural)
kantasi (accusative genitive singular)
kantasi (accusative genitive plural)
kantasi (genitive singular)
kantojesi (genitive plural)
kantaisi (genitive plural rare)
kantaasi (partitive singular)
kantojasi (partitive plural)
kannassasi (inessive singular)
kannoissasi (inessive plural)
kannastasi (elative singular)
kannoistasi (elative plural)
kantaasi (illative singular)
kantoihisi (illative plural)
kannallasi (adessive singular)
kannoillasi (adessive plural)
kannaltasi (ablative singular)
kannoiltasi (ablative plural)
kannallesi (allative singular)
kannoillesi (allative plural)
kantanasi (essive singular)
kantoinasi (essive plural)
kannaksesi (singular translative)
kannoiksesi (plural translative)
kannattasi (abessive singular)
kannoittasi (abessive plural)
kantoinesi (comitative plural)
kantamme (nominative singular)
kantamme (nominative plural)
kantamme (accusative nominative singular)
kantamme (accusative nominative plural)
kantamme (accusative genitive singular)
kantamme (accusative genitive plural)
kantamme (genitive singular)
kantojemme (genitive plural)
kantaimme (genitive plural rare)
kantaamme (partitive singular)
kantojamme (partitive plural)
kannassamme (inessive singular)
kannoissamme (inessive plural)
kannastamme (elative singular)
kannoistamme (elative plural)
kantaamme (illative singular)
kantoihimme (illative plural)
kannallamme (adessive singular)
kannoillamme (adessive plural)
kannaltamme (ablative singular)
kannoiltamme (ablative plural)
kannallemme (allative singular)
kannoillemme (allative plural)
kantanamme (essive singular)
kantoinamme (essive plural)
kannaksemme (singular translative)
kannoiksemme (plural translative)
kannattamme (abessive singular)
kannoittamme (abessive plural)
kantoinemme (comitative plural)
kantanne (nominative singular)
kantanne (nominative plural)
kantanne (accusative nominative singular)
kantanne (accusative nominative plural)
kantanne (accusative genitive singular)
kantanne (accusative genitive plural)
kantanne (genitive singular)
kantojenne (genitive plural)
kantainne (genitive plural rare)
kantaanne (partitive singular)
kantojanne (partitive plural)
kannassanne (inessive singular)
kannoissanne (inessive plural)
kannastanne (elative singular)
kannoistanne (elative plural)
kantaanne (illative singular)
kantoihinne (illative plural)
kannallanne (adessive singular)
kannoillanne (adessive plural)
kannaltanne (ablative singular)
kannoiltanne (ablative plural)
kannallenne (allative singular)
kannoillenne (allative plural)
kantananne (essive singular)
kantoinanne (essive plural)
kannaksenne (singular translative)
kannoiksenne (plural translative)
kannattanne (abessive singular)
kannoittanne (abessive plural)
kantoinenne (comitative plural)
kantansa (nominative singular)
kantansa (nominative plural)
kantansa (accusative nominative singular)
kantansa (accusative nominative plural)
kantansa (accusative genitive singular)
kantansa (accusative genitive plural)
kantansa (genitive singular)
kantojensa (genitive plural)
kantainsa (genitive plural rare)
kantaansa (partitive singular)
kantojaan (partitive plural)
kantojansa (partitive plural)
kannassaan (inessive singular)
kannassansa (inessive singular)
kannoissaan (inessive plural)
kannoissansa (inessive plural)
kannastaan (elative singular)
kannastansa (elative singular)
kannoistaan (elative plural)
kannoistansa (elative plural)
kantaansa (illative singular)
kantoihinsa (illative plural)
kannallaan (adessive singular)
kannallansa (adessive singular)
kannoillaan (adessive plural)
kannoillansa (adessive plural)
kannaltaan (ablative singular)
kannaltansa (ablative singular)
kannoiltaan (ablative plural)
kannoiltansa (ablative plural)
kannalleen (allative singular)
kannallensa (allative singular)
kannoilleen (allative plural)
kannoillensa (allative plural)
kantanaan (essive singular)
kantanansa (essive singular)
kantoinaan (essive plural)
kantoinansa (essive plural)
kannakseen (singular translative)
kannaksensa (singular translative)
kannoikseen (plural translative)
kannoiksensa (plural translative)
kannattaan (abessive singular)
kannattansa (abessive singular)
kannoittaan (abessive plural)
kannoittansa (abessive plural)
kantoineen (comitative plural)
kantoinensa (comitative plural)

[ˈkɑ̝n̪t̪ɑ̝]

From Proto-Finnic *kanta, from Proto-Finno-Ugric *kanta. Cognates include Estonian kand, Erzya кандо (kando, “log, load”), Moksha канда (kanda), Northern Khanty ҳонт (ḥont) and Northern Mansi [script needed] (χānta).


lamination

en-noun

lamination (countable and uncountable, plural laminations)

(topology) A foliation of a closed subset of a manifold by subspaces of one dimension less.


closure

closure (countable and uncountable, plural closures)

From Middle English closure, from Old French closure, from Late Latin clausura, from Latin claudere (“to close”); see clausure and cloture (etymological doublets) and close.

7 THEOREM The closure of any set is the union of the set and the set of its accumulation points.

1955 [Van Nostrand Reinhold], John L. Kelley, General Topology, 2017, Dover, page 42, The closure (𝔗-closure) of a subset A of a topological space (X,𝔗) is the intersection of the members of the family of all closed sets containing A. […]

(topology, of a set) The smallest closed set which contains the given set.


compressible

en-adj

compressible (comparative more compressible, superlative most compressible)

more compressible (comparative)
most compressible (superlative)

LL-Q1860 (eng)-Flame, not lame-compressible.wav

(topology, of a surface embedded in a 3-dimensional manifold) Containing a circle that does not serve as the boundary of a disk that lies in the surface, but does serve as boundary of a disk that lies in the ambient manifold.


head

∧ or #92;land (English symbol name wedge)

land (canonical)
wedge (English name symbol)


Haken

For Wolfgang Haken, who studied these manifolds.

(topology, of a 3-manifold) Irreducible, compact, and containing a non-∂-parallel incompressible surface (besides a sphere or disk).


атлас

atlas (romanization)
атлас (nominative singular)
атластар (nominative plural)
атластың (genitive singular)
атластардың (genitive plural)
атласқа (dative singular)
атластарға (dative plural)
атласты (accusative singular)
атластарды (accusative plural)
атласта (locative singular)
атластарда (locative plural)
атластан (ablative singular)
атластардан (ablative plural)
атласпен (instrumental singular)
атластармен (instrumental plural)

Borrowed from Russian а́тлас (átlas), from Latin Atlas, from Ancient Greek Ἄτλας (Átlas).

Kazakh alphabets#Arabic script
Kazakh alphabets#Cyrillic script
Kazakh alphabets#Latin script
kk:атлас


атлас

atlas (romanization)
атлас (indefinite singular)
атласи (indefinite plural)
атласот (definite singular unspecified)
атласите (definite plural unspecified)
атласов (definite proximal singular)
атласиве (definite plural proximal)
атласон (definite distal singular)
атласине (definite distal plural)
атласу (singular vocative)
атласи (plural vocative)
атласа (count-form plural)

Borrowed from Latin Atlas, from Ancient Greek Ἄτλας (Átlas).


атлас

ru-noun+

а́тлас • (átlas) m inan (genitive а́тласа, nominative plural а́тласы, genitive plural а́тласов, relational adjective а́тласный)

а́тлас (canonical)
átlas (romanization)
а́тласа (genitive)
а́тласы (nominative plural)
а́тласов (genitive plural)
а́тласный (adjective relational)
а́тлас (nominative singular)
а́тласы (nominative plural)
а́тласа (genitive singular)
а́тласов (genitive plural)
а́тласу (dative singular)
а́тласам (dative plural)
а́тлас (accusative singular)
а́тласы (accusative plural)
а́тласом (instrumental singular)
а́тласами (instrumental plural)
а́тласе (prepositional singular)
а́тласах (plural prepositional)
атласъ (alternative)

From Latin Atlas, from Ancient Greek Ἄτλας (Átlas).


атлас

а̀тлас (canonical masculine)
àtlas (romanization)
а̀тлас (nominative singular)
атласи (nominative plural)
а̀тласа (genitive singular)
а̏тла̄са̄ (genitive plural)
атласу (dative singular)
атласима (dative plural)
атлас (accusative singular)
атласе (accusative plural)
атласе (singular vocative)
атласи (plural vocative)
атласу (locative singular)
атласима (locative plural)
атласом (instrumental singular)
атласима (instrumental plural)


oriented

en-adj

oriented (comparative more oriented, superlative most oriented)

more oriented (comparative)
most oriented (superlative)
orientated (alternative)

LL-Q1860 (eng)-Flame, not lame-oriented.wav

(geometry, topology) In any of various technical senses, admitting or being equipped with a notion of handedness (i.e. of distinguishing clockwise and anticlockwise). See Orientability on Wikipedia.Wikipedia


pointlessness

en-noun

pointlessness (countable and uncountable, plural pointlessnesses)

(topology, geometry, uncountable) The quality of not mentioning points.


reuna

reuna (nominative singular)
reunat (nominative plural)
reuna (accusative nominative singular)
reunat (accusative nominative plural)
reunan (accusative genitive singular)
reunat (accusative genitive plural)
reunan (genitive singular)
reunojen (genitive plural)
reunain (genitive plural rare)
reunaa (partitive singular)
reunoja (partitive plural)
reunassa (inessive singular)
reunoissa (inessive plural)
reunasta (elative singular)
reunoista (elative plural)
reunaan (illative singular)
reunoihin (illative plural)
reunalla (adessive singular)
reunoilla (adessive plural)
reunalta (ablative singular)
reunoilta (ablative plural)
reunalle (allative singular)
reunoille (allative plural)
reunana (essive singular)
reunoina (essive plural)
reunaksi (singular translative)
reunoiksi (plural translative)
reunatta (abessive singular)
reunoitta (abessive plural)
reunoin (instructive plural)
See the possessive forms below. (comitative)
reunani (nominative singular)
reunani (nominative plural)
reunani (accusative nominative singular)
reunani (accusative nominative plural)
reunani (accusative genitive singular)
reunani (accusative genitive plural)
reunani (genitive singular)
reunojeni (genitive plural)
reunaini (genitive plural rare)
reunaani (partitive singular)
reunojani (partitive plural)
reunassani (inessive singular)
reunoissani (inessive plural)
reunastani (elative singular)
reunoistani (elative plural)
reunaani (illative singular)
reunoihini (illative plural)
reunallani (adessive singular)
reunoillani (adessive plural)
reunaltani (ablative singular)
reunoiltani (ablative plural)
reunalleni (allative singular)
reunoilleni (allative plural)
reunanani (essive singular)
reunoinani (essive plural)
reunakseni (singular translative)
reunoikseni (plural translative)
reunattani (abessive singular)
reunoittani (abessive plural)
reunoineni (comitative plural)
reunasi (nominative singular)
reunasi (nominative plural)
reunasi (accusative nominative singular)
reunasi (accusative nominative plural)
reunasi (accusative genitive singular)
reunasi (accusative genitive plural)
reunasi (genitive singular)
reunojesi (genitive plural)
reunaisi (genitive plural rare)
reunaasi (partitive singular)
reunojasi (partitive plural)
reunassasi (inessive singular)
reunoissasi (inessive plural)
reunastasi (elative singular)
reunoistasi (elative plural)
reunaasi (illative singular)
reunoihisi (illative plural)
reunallasi (adessive singular)
reunoillasi (adessive plural)
reunaltasi (ablative singular)
reunoiltasi (ablative plural)
reunallesi (allative singular)
reunoillesi (allative plural)
reunanasi (essive singular)
reunoinasi (essive plural)
reunaksesi (singular translative)
reunoiksesi (plural translative)
reunattasi (abessive singular)
reunoittasi (abessive plural)
reunoinesi (comitative plural)
reunamme (nominative singular)
reunamme (nominative plural)
reunamme (accusative nominative singular)
reunamme (accusative nominative plural)
reunamme (accusative genitive singular)
reunamme (accusative genitive plural)
reunamme (genitive singular)
reunojemme (genitive plural)
reunaimme (genitive plural rare)
reunaamme (partitive singular)
reunojamme (partitive plural)
reunassamme (inessive singular)
reunoissamme (inessive plural)
reunastamme (elative singular)
reunoistamme (elative plural)
reunaamme (illative singular)
reunoihimme (illative plural)
reunallamme (adessive singular)
reunoillamme (adessive plural)
reunaltamme (ablative singular)
reunoiltamme (ablative plural)
reunallemme (allative singular)
reunoillemme (allative plural)
reunanamme (essive singular)
reunoinamme (essive plural)
reunaksemme (singular translative)
reunoiksemme (plural translative)
reunattamme (abessive singular)
reunoittamme (abessive plural)
reunoinemme (comitative plural)
reunanne (nominative singular)
reunanne (nominative plural)
reunanne (accusative nominative singular)
reunanne (accusative nominative plural)
reunanne (accusative genitive singular)
reunanne (accusative genitive plural)
reunanne (genitive singular)
reunojenne (genitive plural)
reunainne (genitive plural rare)
reunaanne (partitive singular)
reunojanne (partitive plural)
reunassanne (inessive singular)
reunoissanne (inessive plural)
reunastanne (elative singular)
reunoistanne (elative plural)
reunaanne (illative singular)
reunoihinne (illative plural)
reunallanne (adessive singular)
reunoillanne (adessive plural)
reunaltanne (ablative singular)
reunoiltanne (ablative plural)
reunallenne (allative singular)
reunoillenne (allative plural)
reunananne (essive singular)
reunoinanne (essive plural)
reunaksenne (singular translative)
reunoiksenne (plural translative)
reunattanne (abessive singular)
reunoittanne (abessive plural)
reunoinenne (comitative plural)
reunansa (nominative singular)
reunansa (nominative plural)
reunansa (accusative nominative singular)
reunansa (accusative nominative plural)
reunansa (accusative genitive singular)
reunansa (accusative genitive plural)
reunansa (genitive singular)
reunojensa (genitive plural)
reunainsa (genitive plural rare)
reunaansa (partitive singular)
reunojaan (partitive plural)
reunojansa (partitive plural)
reunassaan (inessive singular)
reunassansa (inessive singular)
reunoissaan (inessive plural)
reunoissansa (inessive plural)
reunastaan (elative singular)
reunastansa (elative singular)
reunoistaan (elative plural)
reunoistansa (elative plural)
reunaansa (illative singular)
reunoihinsa (illative plural)
reunallaan (adessive singular)
reunallansa (adessive singular)
reunoillaan (adessive plural)
reunoillansa (adessive plural)
reunaltaan (ablative singular)
reunaltansa (ablative singular)
reunoiltaan (ablative plural)
reunoiltansa (ablative plural)
reunalleen (allative singular)
reunallensa (allative singular)
reunoilleen (allative plural)
reunoillensa (allative plural)
reunanaan (essive singular)
reunanansa (essive singular)
reunoinaan (essive plural)
reunoinansa (essive plural)
reunakseen (singular translative)
reunaksensa (singular translative)
reunoikseen (plural translative)
reunoiksensa (plural translative)
reunattaan (abessive singular)
reunattansa (abessive singular)
reunoittaan (abessive plural)
reunoittansa (abessive plural)
reunoineen (comitative plural)
reunoinensa (comitative plural)

From Proto-Finnic *rëuna (compare Karelian reuna, Ludian reun, Veps röun), borrowed from Proto-Baltic [Term?] (compare Lithuanian briauna).


obszar

pl-noun

obszar m inan (related adjective obszarowy)

obszarowy (adjective)
obszar (nominative singular)
obszary (nominative plural)
obszaru (genitive singular)
obszarów (genitive plural)
obszarowi (dative singular)
obszarom (dative plural)
obszar (accusative singular)
obszary (accusative plural)
obszarem (instrumental singular)
obszarami (instrumental plural)
obszarze (locative singular)
obszarach (locative plural)
obszarze (singular vocative)
obszary (plural vocative)

→ Belarusian: абшар (abšar)

→ Ukrainian: о́бшар (óbšar)

(topology) domain, region (non-empty connected open set in a topological space)


entourage

/ˈɒn.tʊ.ɹɑːʒ/

/ˈɑ̃ː.tʊ.ɹɑːʒ/

/ˈɑn.tə.ɹɑʒ/

Unadapted borrowing from French entourage, from entourer (“to surround”).

ubor

(topology) A binary relation in a uniform space which generalises the notion of two points being no farther apart than a given fixed distance; a uniform neighbourhood.


metric space

(mathematics, mathematical analysis, topology) Any set on which a metric is defined, giving a distance between any two elements.