kuitukimppu

kuitukimppu (nominative singular)
kuitukimput (nominative plural)
kuitukimppu (accusative nominative singular)
kuitukimput (accusative nominative plural)
kuitukimpun (accusative genitive singular)
kuitukimput (accusative genitive plural)
kuitukimpun (genitive singular)
kuitukimppujen (genitive plural)
kuitukimppua (partitive singular)
kuitukimppuja (partitive plural)
kuitukimpussa (inessive singular)
kuitukimpuissa (inessive plural)
kuitukimpusta (elative singular)
kuitukimpuista (elative plural)
kuitukimppuun (illative singular)
kuitukimppuihin (illative plural)
kuitukimpulla (adessive singular)
kuitukimpuilla (adessive plural)
kuitukimpulta (ablative singular)
kuitukimpuilta (ablative plural)
kuitukimpulle (allative singular)
kuitukimpuille (allative plural)
kuitukimppuna (essive singular)
kuitukimppuina (essive plural)
kuitukimpuksi (singular translative)
kuitukimpuiksi (plural translative)
kuitukimputta (abessive singular)
kuitukimpuitta (abessive plural)
kuitukimpuin (instructive plural)
See the possessive forms below. (comitative)
kuitukimppuni (nominative singular)
kuitukimppuni (nominative plural)
kuitukimppuni (accusative nominative singular)
kuitukimppuni (accusative nominative plural)
kuitukimppuni (accusative genitive singular)
kuitukimppuni (accusative genitive plural)
kuitukimppuni (genitive singular)
kuitukimppujeni (genitive plural)
kuitukimppuani (partitive singular)
kuitukimppujani (partitive plural)
kuitukimpussani (inessive singular)
kuitukimpuissani (inessive plural)
kuitukimpustani (elative singular)
kuitukimpuistani (elative plural)
kuitukimppuuni (illative singular)
kuitukimppuihini (illative plural)
kuitukimpullani (adessive singular)
kuitukimpuillani (adessive plural)
kuitukimpultani (ablative singular)
kuitukimpuiltani (ablative plural)
kuitukimpulleni (allative singular)
kuitukimpuilleni (allative plural)
kuitukimppunani (essive singular)
kuitukimppuinani (essive plural)
kuitukimpukseni (singular translative)
kuitukimpuikseni (plural translative)
kuitukimputtani (abessive singular)
kuitukimpuittani (abessive plural)
kuitukimppuineni (comitative plural)
kuitukimppusi (nominative singular)
kuitukimppusi (nominative plural)
kuitukimppusi (accusative nominative singular)
kuitukimppusi (accusative nominative plural)
kuitukimppusi (accusative genitive singular)
kuitukimppusi (accusative genitive plural)
kuitukimppusi (genitive singular)
kuitukimppujesi (genitive plural)
kuitukimppuasi (partitive singular)
kuitukimppujasi (partitive plural)
kuitukimpussasi (inessive singular)
kuitukimpuissasi (inessive plural)
kuitukimpustasi (elative singular)
kuitukimpuistasi (elative plural)
kuitukimppuusi (illative singular)
kuitukimppuihisi (illative plural)
kuitukimpullasi (adessive singular)
kuitukimpuillasi (adessive plural)
kuitukimpultasi (ablative singular)
kuitukimpuiltasi (ablative plural)
kuitukimpullesi (allative singular)
kuitukimpuillesi (allative plural)
kuitukimppunasi (essive singular)
kuitukimppuinasi (essive plural)
kuitukimpuksesi (singular translative)
kuitukimpuiksesi (plural translative)
kuitukimputtasi (abessive singular)
kuitukimpuittasi (abessive plural)
kuitukimppuinesi (comitative plural)
kuitukimppumme (nominative singular)
kuitukimppumme (nominative plural)
kuitukimppumme (accusative nominative singular)
kuitukimppumme (accusative nominative plural)
kuitukimppumme (accusative genitive singular)
kuitukimppumme (accusative genitive plural)
kuitukimppumme (genitive singular)
kuitukimppujemme (genitive plural)
kuitukimppuamme (partitive singular)
kuitukimppujamme (partitive plural)
kuitukimpussamme (inessive singular)
kuitukimpuissamme (inessive plural)
kuitukimpustamme (elative singular)
kuitukimpuistamme (elative plural)
kuitukimppuumme (illative singular)
kuitukimppuihimme (illative plural)
kuitukimpullamme (adessive singular)
kuitukimpuillamme (adessive plural)
kuitukimpultamme (ablative singular)
kuitukimpuiltamme (ablative plural)
kuitukimpullemme (allative singular)
kuitukimpuillemme (allative plural)
kuitukimppunamme (essive singular)
kuitukimppuinamme (essive plural)
kuitukimpuksemme (singular translative)
kuitukimpuiksemme (plural translative)
kuitukimputtamme (abessive singular)
kuitukimpuittamme (abessive plural)
kuitukimppuinemme (comitative plural)
kuitukimppunne (nominative singular)
kuitukimppunne (nominative plural)
kuitukimppunne (accusative nominative singular)
kuitukimppunne (accusative nominative plural)
kuitukimppunne (accusative genitive singular)
kuitukimppunne (accusative genitive plural)
kuitukimppunne (genitive singular)
kuitukimppujenne (genitive plural)
kuitukimppuanne (partitive singular)
kuitukimppujanne (partitive plural)
kuitukimpussanne (inessive singular)
kuitukimpuissanne (inessive plural)
kuitukimpustanne (elative singular)
kuitukimpuistanne (elative plural)
kuitukimppuunne (illative singular)
kuitukimppuihinne (illative plural)
kuitukimpullanne (adessive singular)
kuitukimpuillanne (adessive plural)
kuitukimpultanne (ablative singular)
kuitukimpuiltanne (ablative plural)
kuitukimpullenne (allative singular)
kuitukimpuillenne (allative plural)
kuitukimppunanne (essive singular)
kuitukimppuinanne (essive plural)
kuitukimpuksenne (singular translative)
kuitukimpuiksenne (plural translative)
kuitukimputtanne (abessive singular)
kuitukimpuittanne (abessive plural)
kuitukimppuinenne (comitative plural)
kuitukimppunsa (nominative singular)
kuitukimppunsa (nominative plural)
kuitukimppunsa (accusative nominative singular)
kuitukimppunsa (accusative nominative plural)
kuitukimppunsa (accusative genitive singular)
kuitukimppunsa (accusative genitive plural)
kuitukimppunsa (genitive singular)
kuitukimppujensa (genitive plural)
kuitukimppuaan (partitive singular)
kuitukimppuansa (partitive singular)
kuitukimppujaan (partitive plural)
kuitukimppujansa (partitive plural)
kuitukimpussaan (inessive singular)
kuitukimpussansa (inessive singular)
kuitukimpuissaan (inessive plural)
kuitukimpuissansa (inessive plural)
kuitukimpustaan (elative singular)
kuitukimpustansa (elative singular)
kuitukimpuistaan (elative plural)
kuitukimpuistansa (elative plural)
kuitukimppuunsa (illative singular)
kuitukimppuihinsa (illative plural)
kuitukimpullaan (adessive singular)
kuitukimpullansa (adessive singular)
kuitukimpuillaan (adessive plural)
kuitukimpuillansa (adessive plural)
kuitukimpultaan (ablative singular)
kuitukimpultansa (ablative singular)
kuitukimpuiltaan (ablative plural)
kuitukimpuiltansa (ablative plural)
kuitukimpulleen (allative singular)
kuitukimpullensa (allative singular)
kuitukimpuilleen (allative plural)
kuitukimpuillensa (allative plural)
kuitukimppunaan (essive singular)
kuitukimppunansa (essive singular)
kuitukimppuinaan (essive plural)
kuitukimppuinansa (essive plural)
kuitukimpukseen (singular translative)
kuitukimpuksensa (singular translative)
kuitukimpuikseen (plural translative)
kuitukimpuiksensa (plural translative)
kuitukimputtaan (abessive singular)
kuitukimputtansa (abessive singular)
kuitukimpuittaan (abessive plural)
kuitukimpuittansa (abessive plural)
kuitukimppuineen (comitative plural)
kuitukimppuinensa (comitative plural)

kuitu (“fiber”) + kimppu (“bundle”), calque of English fiber bundle


locally compact group

en-noun

locally compact group (plural locally compact groups)

Indeed, if there is one property of locally compact groups more responsible than any other for the rich positive content of their representation theory, it is their possession of left-invariant and right-invariant (Haar) measures. The connection between the representation theory of a locally compact group and that of general Banach algebras proceeds directly from Lebesgue integration with respect to Haar measure on the group.

1988, J. M. G. Fell, R. S. Doran, Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Volume 1, Academic Press, page 63:

A locally compact group G is called Lie projective if it is the projective limit #92;textstyle#92;underset#123;#92;leftarrow#125;#123;#92;lim#125;#95;#123;#92;alpha#92;in#92;mathbb#123;A

2012, H. Heyer, Probability Measures on Locally Compact Groups, Springer, page 12:

Let G be a locally compact group and H a closed subgroup of G, and suppose that #92;pi and #92;tau are irreducible representations of G and H, respectively.

2013, Eberhard Kaniuth, Keith F. Taylor, Induced Representations of Locally Compact Groups, Cambridge University Press, page 269:

(topology) A topological group whose underlying topology is both locally compact and Hausdorff.

lokalkompakte Gruppe

topological group whose topology is locally compact and Hausdorff


algebraic analysis

The area of study in algebraic geometry began as a research programme, instigated in 1959 by Japanese mathematician Mikio Sato.

1986, Goro Kato (translator), Masaki Kashiwara, Takahiro Kawai, Tatsuo Kimura, Foundations of Algebraic Analysis, Princeton Universty Press, https://books.google.com.au/books?id=qYUrDgAAQBAJ&printsec=frontcover&dq=%22algebraic+analysis%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwiK5MSlvsLsAhWXbn0KHbPuBPQQ6AEwAnoECAYQAg#v=onepage&q=%22algebraic%20analysis%22&f=false.

In their classical work [123], Kashiwara, Kawai, and Kimura pointedly observe that the Japanese algebraic analysis is really the algebraic analysis in the tradition of Euler; we may add that what we mean by algebraic microlocal analysis is the successful attempt to adapt the methods of abstract algebraic geometry to the non-commutative setting in which the base ring is now the ring of variable coefficients^([sic]) partial differential operators.

1999, Goro Kato, Daniele C. Struppa, Fundamentals of Algebraic Microlocal Analysis, Marcel Dekker, page v:

2008, Yoshitsugu Takei, The work of T. Kawai on exact WKB analysis, T. Aoki, H. Majima, Y. Takei, N. Tose (editors), Algebraic Analysis of Differential Equations, Springer, page 19,
Thus Kawai has been engaged mainly in the research of exact WKB analysis or algebraic analysis of singular perturbation theory since 1989.

partial differential equation
partial differential equation

(algebraic geometry, algebraic topology) The study of systems of linear partial differential equations, using techniques from sheaf theory and complex analysis to examine functions and certain generalisations of functions (such as hyperfunctions and microfunctions).


initial topology

initial topology (plural initial topologies)

topological space
topological space#English

(topology) Given a set X, a family of topological spaces (M#95;i,T#95;i)#95;#123;i#92;inI#125; and a family of functions f#95;i#58;X#92;toM#95;i, the initial topology is the coarsest topology on X such that all f#95;i are continuous.


final topology

final topology (plural final topologies)

(topology) Given a set X, a family of topological spaces (M#95;i,T#95;i)#95;#123;i#92;inI#125; and a family of functions f#95;i#58;M#95;i#92;toX, the final topology is the finest topology on X such that all f#95;i are continuous.


closed loop

(topology) A path whose initial point is equal to its terminal point.


chain group

kth chain group (canonical)
chain groups (plural)

(algebraic topology) A free abelian group generated by all the k-dimensional oriented simplices of a given simplicial complex.


homology group

kth homology group (plural homology groups)

kth homology group (canonical)
homology groups (plural)

(algebraic topology) The quotient group of the kth cycle group modulo the kth boundary group (derived from the chain complex of, e.g., a given simplicial complex).


boundary group

kth boundary group (plural boundary groups)

kth boundary group (canonical)
boundary groups (plural)

boundary homomorphism
boundary homomorphism

(algebraic topology) The image of the (k + 1)ᵗʰ boundary homomorphism (for a given chain complex).


cycle group

kth cycle group (canonical)
cycle groups (plural)

(algebraic topology) The kernel of the kᵗʰ boundary homomorphism (of a given chain complex).


boundary homomorphism

kth boundary homomorphism (plural boundary homomorphisms)

kth boundary homomorphism (canonical)
boundary homomorphisms (plural)

(algebraic topology, in a simplicial chain complex) A group homomorphism on the group of simplicial k-chains induced by mapping each oriented k-simplex to a particular formal sum of its faces.

(algebraic topology, in greater generality) A homomorphism that operates on the kth element in a chain complex.


randpunkt

randpunkt (indefinite nominative singular)
randpunkts (genitive indefinite singular)
randpunkten (definite nominative singular)
randpunktens (definite genitive singular)
randpunkter (indefinite nominative plural)
randpunkters (genitive indefinite plural)
randpunkterna (definite nominative plural)
randpunkternas (definite genitive plural)

(mathematics, topology) boundary point (element of the boundary of a set)


Alexander horned sphere

Alexander horned sphere (plural Alexander horned spheres)

(topology) A pathological object, a certain embedding of a sphere in three-dimensional Euclidean space, obtained by various modifications of a torus.


exact cover

A finite set #92;#123;S(#92;alpha#95;i,#92;beta#95;i)#92;vert 1#92;lei#92;lem#92;#125; is called an (eventual) exact cover if every (sufficiently large) positive integer occurs in exactly one S(#92;alpha#95;i,#92;beta#95;i). If #92;#123;S(#92;alpha#95;i,#92;beta#95;i)#92;#125;#95;#123;i#61;1#125;ᵐ is an eventual exact cover, then #92;textstyle#92;sum#95;#123;i#61;1#125;ᵐ#123;#92;alpha#95;i#123;-1

2000, R. Tijdeman, “Exact covers of balanced sequences and Fraenkel's conjecture”, in F. Halter-Koch, Robert F. Tichy, editors, Algebraic Number Theory and Diophantine Analysis: Proceedings of the International Conference, Walter de Gruyter, page 468:

2011, R. Lu, S. Liu, J. Zhang, Searching for Doubly Self-orthogonal Latin Squares, Jimmy Lee (editor), Principles and Practice of Constraint Programming: 17th International Conference CP 2011, Proceedings, Springer, LNCS 6876, page 542,
It is straightforward to use clique algorithms to construct a (partial) solution of a given combinatorial problem which is represented as a set system. If the solution of the combinatorial problem corresponds to the exact cover of the set system, a substantially more efficient algorithm can be utilized because of this property.

(topology, combinatorics) Given a collection S of subsets of a set X, a subcollection S^* of S such that each element of X is contained in exactly one subset in S^*.

exakte Überdeckung

Collection of subsets such that each element of the original set is contained in exactly one subset


위상공간

wisanggonggan (romanization)
位相空間 (hanja)

[ɥisʰa̠ŋɡo̞ŋɡa̠n]

[ysʰa̠ŋɡo̞ŋɡa̠n]

Sino-Korean word from 位相空間, from 位相 + 空間.


merotopy

An affirmative answer was given by Simon in a recent paper on natural merotopies.

1980, Topology (issue 23, part 1, page 608)

That μ_A satisfies the axioms of a merotopy is easily seen.

2004, Categorical Structures and Their Applications: Proceedings of the North-West European Category Seminar, Berlin, Germany, 28-29 March 2003, page 63:

(topology) The set of all subsets of a topological space such that, for some element in that space every neighbourhood of that element contains a member of the subset.


Brunnian braid

(topology) A braid that becomes trivial upon removal of any one of its strings.


bottiglia di Klein

it-noun

bottiglia di Klein f (plural bottiglie di Klein)

(topology) Klein bottle (closed surface)


otre di Klein

bottiglia di Klein
bottiglia di Klein#Italian

(topology) synonym of bottiglia di Klein (“Klein bottle”)


point d'accumulation

fr-noun

point d'accumulation m (plural points d'accumulation)

(topology) accumulation point, limit point


spatial locale

(topology) A locale which originates from a topological space.


Stone-Čech compactification

en-noun

Stone-Čech compactification (countable and uncountable, plural Stone-Čech compactifications)

Stone-Čech compactifications (plural)
Čech-Stone compactification (alternative)

Named after Marshall Stone and Eduard Čech, who wrote on the topic in 1937.

A technique for constructing a universal map from a topological space to a compact Hausdorff space.

The space obtained by using this technique.


Čech-Stone compactification

Čech-Stone compactification (countable and uncountable, plural Čech-Stone compactifications)

Stone-Čech compactification
Stone-Čech compactification#English

Alternative form of Stone-Čech compactification.


nadprzestrzeń

pl-noun

nadprzestrzeń f (related adjective nadprzestrzenny)

nadprzestrzenny (adjective)
nadprzestrzeń (nominative singular)
nadprzestrzeni (genitive singular)
nadprzestrzeni (dative singular)
nadprzestrzeń (accusative singular)
nadprzestrzenią (instrumental singular)
nadprzestrzeni (locative singular)
nadprzestrzeni (singular vocative)

(topology) hyperspace (space within which some of its elements form another topological space)


wstęga Mobiusa

wstęga Mobiusa (nominative singular)
wstęgi Mobiusa (nominative plural)
wstęgi Mobiusa (genitive singular)
wstąg Mobiusa (genitive plural)
wstędze Mobiusa (dative singular)
wstęgom Mobiusa (dative plural)
wstęgę Mobiusa (accusative singular)
wstęgi Mobiusa (accusative plural)
wstęgą Mobiusa (instrumental singular)
wstęgami Mobiusa (instrumental plural)
wstędze Mobiusa (locative singular)
wstęgach Mobiusa (locative plural)
wstęgo Mobiusa (singular vocative)
wstęgi Mobiusa (plural vocative)
wstęga Möbiusa (alternative)

Literally, “Mobius' ribbon,” named after German mathematician August Ferdinand Möbius.


butelka Kleina

butelka Kleina (nominative singular)
butelki Kleina (nominative plural)
butelki Kleina (genitive singular)
butelek Kleina (genitive plural)
butelce Kleina (dative singular)
butelkom Kleina (dative plural)
butelkę Kleina (accusative singular)
butelki Kleina (accusative plural)
butelką Kleina (instrumental singular)
butelkami Kleina (instrumental plural)
butelce Kleina (locative singular)
butelkach Kleina (locative plural)
butelko Kleina (singular vocative)
butelki Kleina (plural vocative)

Literally, “Klein's bottle,” named after German mathematician Felix Klein.


connecting homomorphism

en-noun

connecting homomorphism (plural connecting homomorphisms)

(homological algebra) The homomorphism constructed by the snake lemma, leading to a particular exact sequence of kernels and cokernels.

(algebraic topology) Such a homomorphism in the context of exact sequences of chain complexes, leading to a long exact sequence of homology groups.


skeletoid

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 ^([sic]) 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 structure that captures the essential topological information of a space.


sequentially compact

(topology, of a topological space) Such that every sequence in the space has a convergent subsequence. In a metric space, this is equivalent to being compact (sense 4.1).

jonokompakti

topology: every sequence in the space has a convergent subsequence


time-one map

In [5], Brin and Pesin investigated the dynamical properties of diffeomorphisms like the time-one map of an Anosov flow, which they called "partially hyperbolic."

1995, Anne Marie Wilkinson, Stable Ergodicity of the Time-one Map of a Geodesic Flow, page 12:

(mathematics, topology) A type of diffeomorphism that represents the evolution of a dynamical system over a unit time interval, where each point in the system's phase space is mapped to another point after one unit of time has passed.


Urysohn's lemma

Named after the mathematician Pavel Samuilovich Urysohn.

(topology) A lemma stating that a topological space is normal if and only if any two disjoint closed subsets can be separated by a continuous function.


bouquet of spheres

bouquet of spheres (plural bouquets of spheres)

(topology) A wedge product of two or more spheres joined at a distinguished point, usually the equator.


лабда

head

лабда (labda) f (diminutive лабдочка, related adjective лабдов)

labda (romanization)
лабдочка (diminutive)
лабдов (adjective)
лабда (nominative singular)
лабди (nominative plural)
лабди (genitive singular)
лабдох (genitive plural)
лабди (dative singular)
лабдом (dative plural)
лабду (accusative singular)
лабди (accusative plural)
лабду (instrumental singular)
лабдами (instrumental plural)
лабди (locative singular)
лабдох (locative plural)
лабдо (singular vocative)
лабди (plural vocative)

Borrowed from Hungarian labda, ultimately from Proto-Slavic *lopъta, whence Carpathian Rusyn ло́пта (lópta) and Slovak lopta. Displaced Old Slovak lopta.


przestrzeń polska

przestrzeń polska (nominative singular)
przestrzenie polskie (nominative plural)
przestrzeni polskiej (genitive singular)
przestrzeni polskich (genitive plural)
przestrzeni polskiej (dative singular)
przestrzeniom polskim (dative plural)
przestrzeń polską (accusative singular)
przestrzenie polskie (accusative plural)
przestrzenią polską (instrumental singular)
przestrzeniami polskimi (instrumental plural)
przestrzeni polskiej (locative singular)
przestrzeniach polskich (locative plural)
przestrzeni polska (singular vocative)
przestrzenie polskie (plural vocative)

Internationalism; compare English Polish space, German Polnischer Raum, Spanish espacio polaco. Named after Polish mathematicians due to the fact they were first extensively studied by Polish topologists and logicians, such as Sierpiński, Kuratowski, and Tarski.

(topology) Polish space (separable, completely metrizable topological space)


𝐙

(algebra, topology, order theory) The set of integers with some usual structure.


closure operator

en-noun

closure operator (plural closure operators)

1997 [Kluwer Academic], R. Friĉ, History of Sequential Convergence Spaces, C. E. Aull, R. Lowen (editors), Handbook of the History of General Topology, Volume 1, Springer, page 346,
Let u be a closure operator on X satisfying the first three closure axioms: u(U∪B)=uU∪uB,A⊂u(A),u empty = empty .

(mathematics, topology, algebra, "on" a set S) A function which maps any subset X of S onto another such subset (or possibly X itself) called the closure of X (thus providing a mathematical means to define closure).