Definitions

# Weakly contractible

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

## Property

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

## Example

Define $S^infty$ to be the inductive limit of the spheres $S^n, nge 1$. 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.

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