- contractible space
- мат.стягиваемое пространство
English-Russian scientific dictionary. 2008.
contractible space
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Contractible space — In mathematics, a topological space X is contractible if the identity map on X is null homotopic, i.e. if it is homotopic to some constant map.[1][2] Intuitively, a contractible space is one that can be continuously shrunk to a point. A… … Wikipedia
Classifying space — In mathematics, specifically in homotopy theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG (i.e. a topological space for which all its homotopy groups are trivial) by a free action of G. It… … Wikipedia
Classifying space for U(n) — In mathematics, the classifying space for the unitary group U(n) is a space B(U(n)) together with a universal bundle E(U(n)) such that any hermitian bundle on a paracompact space X is the pull back of E by a map X → B unique up to homotopy. This… … Wikipedia
Contractibility of unit sphere in Hilbert space — In topology, it is a surprising fact that the unit sphere in (infinite dimensional) Hilbert space is a contractible space, sinceno finite dimensional spheres are contractible.This can be demonstrated in several different ways. Topological proof… … Wikipedia
Connected space — For other uses, see Connection (disambiguation). Connected and disconnected subspaces of R² The green space A at top is simply connected whereas the blue space B below is not connected … Wikipedia
Acyclic space — In mathematics, an acyclic space is a topological space X in which cycles are always boundaries, in the sense of homology theory. This implies that the integral homology groups in all dimensions of X are isomorphic to the corresponding homology… … Wikipedia
Quotient space — In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or gluing together certain points of a given space. The points to be identified are specified … Wikipedia
classifying space — noun A topological space that is the quotient of a free action (of the specified group) on a weakly contractible space … Wiktionary
CAT(k) space — In mathematics, a CAT( k ) space is a specific type of metric space. Intuitively, triangles in a CAT( k ) space are slimmer than corresponding model triangles in a standard space of constant curvature k . In a CAT( k ) space, the curvature is… … Wikipedia
Weakly contractible — In mathematics, a topological space is said to be weakly contractible if all of its homotopy groups are trivial.PropertyIt follows from Whitehead s Theorem that if a CW complex is weakly contractible then it is contractible.ExampleDefine S^infty… … Wikipedia
Locally simply connected space — In mathematics, a locally simply connected space is a topological space that admits a basis of simply connected sets. Every locally simply connected space is also locally path connected and locally connected.The circle is an example of a locally… … Wikipedia
