homology
noun
Forms homologies
- noun (geometry, projective geometry) specifically, such relationship in the context of the geometry of perspective.
- noun (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. “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.”
- noun (topology, algebraic topology) 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.
- noun (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. “Because of their connection with both homology and cohomology, chain complexes are an important topic of study in homological algebra.”
- noun (chemistry) The relationship, between elements, of being in the same group of the periodic table.
- noun (organic chemistry) The relationship, between organic compounds, of being in the same homologous series.
- noun (biology, psychology) The relationship, between characteristics or behaviours, of having a shared evolutionary or developmental origin;
Antonyms
Etymology
From Latin homologia, from Ancient Greek ὁμολογία (homología, “agreement, assent”); compare French homologie. By surface analysis, homo- + -logy.
In 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.
Webster’s 1913
- noun The quality of being homologous; correspondence; relation; as, the homologyof similar polygons.
- noun Correspondence or relation in type of structure in contradistinction to similarity of function; as, the relation in structure between the leg and arm of a man; or that between the arm of a man, the fore leg of a horse, the wing of a bird, and the fin of a fish, all these organs being modifications of one type of structure.
Etymology [Gr. Homologous.]
Sources: Wiktionary · Webster’s 1913 — from the Wiktionary entry “homology”, CC BY-SA 4.0. Details