See homology on Wiktionary
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"etymology_text": "From homo- + -logy.\nIn topology, first used by French polymath Henri Poincaré, in the sense (close to what is now called a bordism) of a relation between manifolds mapped into a reference manifold: that is, the property of such manifolds that they form the boundary of a higher-dimensional manifold inside the reference manifold. Poincaré's version was eventually replaced by the more general singular homology, which is what mathematicians now mean by homology.",
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"text": "1863, George Salmon, A Treatise on Conic Sections, Longman, Brown, Green, Longman, and Roberts, 4th Edition, page 61,\nTwo triangles are said to be homologous, when the intersections of the corresponding sides lie on the same right line called the axis of homology: prove that the lines joining the corresponding vertices meet in a point [called the centre of homology]."
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"text": "1885, Charles Leudesdorf (translator), Luigi Cremona, Elements of Projective Geometry, Oxford University Press (Clarendon Press), page 11,\nTwo corresponding straight lines therefore always intersect on a fixed straight line, which we may call s; thus the given figures are in homology, O being the centre, and s the axis, of homology."
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"text": "If the homology centre lies on the homology axis, the homology is said to be singular or parabolic; otherwise, it is called non-singular or hyperbolic.",
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"An automorphism of the projective plane (representing a perspective projection) that leaves all the points of some straight line (the homology axis) fixed and maps all the lines through some single point (the homology centre) onto themselves."
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"(geometry, projective geometry) An automorphism of the projective plane (representing a perspective projection) that leaves all the points of some straight line (the homology axis) fixed and maps all the lines through some single point (the homology centre) onto themselves."
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"ref": "2000, Sibe Mardešić, Strong Shape and Homology, Springer, page v:",
"text": "One encounters a similar situation in homology theory. Beside singular homology, which is a homotopy invariant, and Čech homology, which is a shape invariant, there exists strong homology, which is a strong shape invariant. In the special case of metric compacta, this homology was introduced by N.E. Steenrod in 1940 and is often referred to as the Steenrod homology.",
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"ref": "2002, Nikolai Saveliev, Invariants of Homology 3-Spheres, Springer, page 2:",
"text": "Brieskorn homology spheres are a special case of Siefert fibered homology spheres.",
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"A general way of associating a sequence of algebraic objects, such as abelian groups or modules, to a sequence of topological spaces; also used attributively: see Usage notes below."
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"text": "Because of their connection with both homology and cohomology, chain complexes are an important topic of study in homological algebra.",
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"Given a chain complex {Gₙ} and its associated set of homomorphisms {Hₙ}, the rule which explains how each Hₙ maps Gₙ into the kernel of Gₙ₊₁."
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"(algebra) Given a chain complex {Gₙ} and its associated set of homomorphisms {Hₙ}, the rule which explains how each Hₙ maps Gₙ into the kernel of Gₙ₊₁."
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{
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[
"homologous",
"homologous"
],
[
"genetics",
"genetics"
],
[
"series",
"series"
],
[
"base",
"base"
],
[
"gene",
"gene"
]
],
"raw_glosses": [
"The relationship of being homologous; a homologous relationship.",
"(genetics) The presence of the same series of bases in different but related genes."
],
"tags": [
"countable",
"uncountable"
],
"topics": [
"biology",
"genetics",
"medicine",
"natural-sciences",
"sciences"
]
},
{
"categories": [
"en:Anthropology"
],
"glosses": [
"The relationship of being homologous; a homologous relationship.",
"The relationship, between temporally separated human beliefs, practices or artefacts, of possessing shared characteristics attributed to genetic or historical links to a common ancestor."
],
"links": [
[
"homologous",
"homologous"
],
[
"anthropology",
"anthropology"
],
[
"temporally",
"temporally"
]
],
"raw_glosses": [
"The relationship of being homologous; a homologous relationship.",
"(anthropology) The relationship, between temporally separated human beliefs, practices or artefacts, of possessing shared characteristics attributed to genetic or historical links to a common ancestor."
],
"tags": [
"countable",
"uncountable"
],
"topics": [
"anthropology",
"human-sciences",
"sciences"
]
}
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "homologous relationship",
"word": "samankaltaisuus"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "homologous relationship",
"word": "homologia"
},
{
"code": "ga",
"lang": "Irish",
"sense": "homologous relationship",
"tags": [
"feminine"
],
"word": "homalógacht"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "homologous relationship",
"tags": [
"feminine"
],
"word": "homologia"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "homologous relationship",
"tags": [
"feminine"
],
"word": "omologie"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "geometry: automorphism representing a perspective projection",
"word": "samankaltaisuus"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "geometry: automorphism representing a perspective projection",
"word": "homologia"
},
{
"code": "ga",
"lang": "Irish",
"sense": "geometry: automorphism representing a perspective projection",
"tags": [
"feminine"
],
"word": "homalógacht"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "geometry: automorphism representing a perspective projection",
"tags": [
"feminine"
],
"word": "homologia"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "geometry: automorphism representing a perspective projection",
"tags": [
"feminine"
],
"word": "omologie"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "tóngdiào",
"sense": "algebraic topology: way of associating a sequence of groups to a sequence of topological spaces",
"word": "同调"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "tóngdiàolùn",
"sense": "algebraic topology: way of associating a sequence of groups to a sequence of topological spaces",
"word": "同调论"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "algebraic topology: way of associating a sequence of groups to a sequence of topological spaces",
"word": "homologia"
},
{
"code": "ga",
"lang": "Irish",
"sense": "algebraic topology: way of associating a sequence of groups to a sequence of topological spaces",
"tags": [
"feminine"
],
"word": "homalógacht"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "algebraic topology: way of associating a sequence of groups to a sequence of topological spaces",
"tags": [
"feminine"
],
"word": "homologia"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "tóngdiào",
"sense": "algebra: rule by which each member of a chain complex maps into the kernel of the next",
"word": "同调"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "tóngdiàoqún",
"sense": "algebra: rule by which each member of a chain complex maps into the kernel of the next",
"word": "同调群"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "algebra: rule by which each member of a chain complex maps into the kernel of the next",
"word": "homologia"
},
{
"code": "ga",
"lang": "Irish",
"sense": "algebra: rule by which each member of a chain complex maps into the kernel of the next",
"tags": [
"feminine"
],
"word": "homalógacht"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "algebra: rule by which each member of a chain complex maps into the kernel of the next",
"tags": [
"feminine"
],
"word": "homologia"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "biology, psychology: relationship of having a common evolutionary or developmental origin",
"word": "homologia"
},
{
"code": "ga",
"lang": "Irish",
"sense": "biology, psychology: relationship of having a common evolutionary or developmental origin",
"tags": [
"feminine"
],
"word": "homalógacht"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "biology, psychology: relationship of having a common evolutionary or developmental origin",
"word": "omologie"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "chemistry: relationship of being in the same group of the periodic table",
"word": "homologia"
},
{
"code": "fr",
"lang": "French",
"sense": "chemistry: relationship of being in the same group of the periodic table",
"word": "homologie"
},
{
"code": "ga",
"lang": "Irish",
"sense": "chemistry: relationship of being in the same group of the periodic table",
"tags": [
"feminine"
],
"word": "homalógacht"
},
{
"code": "it",
"lang": "Italian",
"sense": "chemistry: relationship of being in the same group of the periodic table",
"word": "omologia"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "chemistry: relationship of being in the same group of the periodic table",
"word": "homologia"
},
{
"code": "es",
"lang": "Spanish",
"sense": "chemistry: relationship of being in the same group of the periodic table",
"word": "homología"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "organic chemistry: relationship of being in the same homologous series",
"word": "homologia"
},
{
"code": "fr",
"lang": "French",
"sense": "organic chemistry: relationship of being in the same homologous series",
"word": "homologie"
},
{
"code": "ga",
"lang": "Irish",
"sense": "organic chemistry: relationship of being in the same homologous series",
"tags": [
"feminine"
],
"word": "homalógacht"
},
{
"code": "it",
"lang": "Italian",
"sense": "organic chemistry: relationship of being in the same homologous series",
"word": "omologia"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "organic chemistry: relationship of being in the same homologous series",
"word": "homologia"
},
{
"code": "es",
"lang": "Spanish",
"sense": "organic chemistry: relationship of being in the same homologous series",
"word": "homología"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "genetics: presence of the same series of bases in related genes",
"word": "homologia"
},
{
"code": "fr",
"lang": "French",
"sense": "genetics: presence of the same series of bases in related genes",
"word": "homologie"
},
{
"code": "ga",
"lang": "Irish",
"sense": "genetics: presence of the same series of bases in related genes",
"tags": [
"feminine"
],
"word": "homalógacht"
},
{
"code": "it",
"lang": "Italian",
"sense": "genetics: presence of the same series of bases in related genes",
"word": "omologia"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "genetics: presence of the same series of bases in related genes",
"word": "homologia"
},
{
"code": "es",
"lang": "Spanish",
"sense": "genetics: presence of the same series of bases in related genes",
"word": "homología"
}
],
"wikipedia": [
"Henri Poincaré",
"Homology",
"MathWorld",
"singular homology"
],
"word": "homology"
}
Download raw JSONL data for homology meaning in All languages combined (19.2kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.