Contractible

Some articles on contractible:

Classifying Space - Motivation
... another way to specify the condition on X is that the universal cover Y of X is contractible ... higher homotopy groups vanish the fundamental idea is, given G, to find such a contractible space Y on which G acts freely ... remark that an infinite cyclic group C acts freely on the real line R, which is contractible ...
CAT(k) Space - Properties of CAT(k) Spaces
... The d-balls in X of radius less than Dk are contractible ... these properties that, for k ≤ 0, the universal cover of every CAT(k) space is contractible in particular, the higher homotopy groups of such a space are trivial ... example of the n-sphere Sn shows, there is, in general, no hope for a CAT(k) space to be contractible if k is strictly positive ...
Locally Contractible Spaces
... A topological space is locally contractible if every point has a local base of contractible neighborhoods ... Contractible spaces are not necessarily locally contractible nor vice-versa ... For example, the comb space is contractible but not locally contractible (if it were, it would be locally connected which it is not) ...
Projective Unitary Group - The Topology of PU(H) - PU(H) Is A Classifying Space For Circle Bundles
... This means that U(H) is weakly contractible, and an additional argument shows that it is actually contractible ... finite-dimensional cousins U(n) and their limit U(∞) under the inclusion maps which are not contractible admitting homotopically nontrivial continuous mappings onto U(1) given by the determinant of matrices ... Thus U is a contractible space with a U(1) action, which identifies it as EU(1) and the space of U(1) orbits as BU(1), the classifying space for U(1) ...
Contractible Space - Examples and Counterexamples
... Any Euclidean space is contractible, as is any star domain on a Euclidean space ... The Whitehead manifold is contractible ... Spheres of any finite dimension are not contractible ...