Weakly contractible

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

Property[edit]

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

Example[edit]

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.

References[edit]