extraordinary homology

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• Homology theory — In mathematics, homology theory is the axiomatic study of the intuitive geometric idea of homology of cycles on topological spaces. It can be broadly defined as the study of homology theories on topological spaces. Simple explanation At the… …   Wikipedia

• Special homology — Special Spe cial, a. [L. specialis, fr. species a particular sort, kind, or quality: cf. F. sp[ e]cial. See {Species}, and cf. {Especial}.] 1. Of or pertaining to a species; constituting a species or sort. [1913 Webster] A special is called by… …   The Collaborative International Dictionary of English

• Eilenberg–Steenrod axioms — In mathematics, specifically in algebraic topology, the Eilenberg–Steenrod axioms are properties that homology theories of topological spaces have in common. The quintessential example of a homology theory satisfying the axioms is singular… …   Wikipedia

• Eilenberg-Steenrod axioms — In mathematics, specifically in algebraic topology, the Eilenberg Steenrod axioms are properties that homology theories of topological spaces have in common. The quintessential example of a homology theory satisfying the axioms is singular… …   Wikipedia

• List of cohomology theories — This is a list of some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra. For other sorts of homology theories see the links at… …   Wikipedia

• Pseudocircle — The pseudocircle is the finite topological space X consisting of four distinct points {a,b,c,d} with the following non Hausdorff topology::left{{a,b,c,d},{a,b,c},{a,b,d},{a,b},{a},{b},emptyset ight} X is highly pathological from the viewpoint of… …   Wikipedia

• Cobordism — A cobordism (W;M,N). In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary of a manifold. Two manifolds are cobordant if their disjoint… …   Wikipedia

• Spectral sequence — In the area of mathematics known as homological algebra, especially in algebraic topology and group cohomology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a… …   Wikipedia

• evolution — evolutional, adj. evolutionally, adv. /ev euh looh sheuhn/ or, esp. Brit., /ee veuh /, n. 1. any process of formation or growth; development: the evolution of a language; the evolution of the airplane. 2. a product of such development; something… …   Universalium

• Mayer–Vietoris sequence — In mathematics, particularly algebraic topology and homology theory, the Mayer–Vietoris sequence is an algebraic tool to help compute algebraic invariants of topological spaces, known as their homology and cohomology groups. The result is due to… …   Wikipedia

• Cohomology — In mathematics, specifically in algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co chain complex. That is, cohomology is defined as the abstract study of cochains, cocycles, and coboundaries.… …   Wikipedia