Weakly contractible

From Wikipedia, the free encyclopedia

[edit] Definition

In mathematics, a topological space is said to be weakly contractible if all of its homotopy groups are trivial.

[edit] Property

It follows from Whitehead's Theorem that if a CW-complex is weakly contractible then it is contractible.

[edit] Example

Define S^\infty to be the inductive limit of the spheres S^n, n\ge 1. Then this space is weakly contractible. Since S^\infty is moreover a CW-complex, it is also contractible. See Contractibility of unit sphere in Hilbert space for more.

 This topology-related article is a stub. You can help Wikipedia by expanding it.