- homotopy
Wikipedia foundation.
homotopy
Look at other dictionaries:
Homotopy — This article is about topology. For chemistry, see Homotopic groups. The two dashed paths shown above are homotopic relative to their endpoints. The animation represents one possible homotopy. In topology, two continuous functions from one… … Wikipedia
homotopy — /heuh mot euh pee, hoh /, n., pl. homotopies. Math. the relation that exists between two mappings in a topological space if one mapping can be deformed in a continuous way to make it coincide with the other. [1915 20; HOMO + topy ( < Gr tóp(os)… … Universalium
Homotopy groups of spheres — In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, which reflect, in algebraic terms, the structure… … Wikipedia
Homotopy group — In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The base point preserving maps from an n dimensional sphere (with base point) into a given space (with base point) are collected into equivalence… … Wikipedia
Homotopy category — In mathematics, a homotopy category is a category whose objects are topological spaces and whose morphisms are homotopy classes of continuous functions. The homotopy category of all topological spaces is often denoted hTop or Toph.Homotopy… … Wikipedia
Homotopy lifting property — In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property (also known as the right lifting property or the covering homotopy axiom) is a technical condition on a continuous function from a… … Wikipedia
Homotopy category of chain complexes — In homological algebra in mathematics, the homotopy category K(A) of chain complexes in an additive category A is a framework for working with chain homotopies and homotopy equivalences. It lies intermediate between the category of chain… … Wikipedia
Homotopy extension property — In mathematics, in the area of algebraic topology, the homotopy extension property indicates when a homotopy can be extended to another one, so that the original homotopy is simply the restriction of the extended homotopy.DefinitionGiven A subset … Wikipedia
Homotopy to Marie — Infobox Album Name = Homotopy to Marie Type = Album Artist = Nurse With Wound Released = 1982 Recorded = 1981 82 Genre = Industrial, Experimental Length = 65:30 Label = United Dairies Producer = Steven Stapleton Reviews = *Allmusic (3.5/5)… … Wikipedia
Homotopy sphere — In algebraic topology, a branch of mathematics, a homotopy sphere is an n manifold homotopy equivalent to the n sphere. It thus has the same homotopy groups and the same homology groups, as the n sphere. So every homotopy sphere is an homology… … Wikipedia
Homotopy fiber — In mathematics, especially homotopy theory, the homotopy fiber is part of a construction of associating to an arbitrary continuous function of topological spaces f colon A o B a fibration.In particular, given such a map, define E f to be the set… … Wikipedia
