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

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

Define $S^{\infty}$ to be the inductive limit of the spheres $S^{n}, n \geq 1$ . 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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+In [[mathematics]], a [[topological space]] is said to be '''weakly contractible''' if all of its [[homotopy group]]s are trivial.
+==Property==
+It follows from [[Whitehead theorem|Whitehead's Theorem]] that if a [[CW-complex]] is weakly contractible then it is [[contractible]].
+==Example==
+Define <math>S^\infty</math> to be the [[inductive limit]] of the spheres <math>S^n, n\ge 1</math>. Then this space is weakly contractible. Since <math>S^\infty</math> is moreover a CW-complex, it is also contractible.  See [[Contractibility of unit sphere in Hilbert space]] for more.
+==References==
+*{{Springer|id=h/h047940|title=Homotopy type}}
+{{DEFAULTSORT:Weakly Contractible}}
+[[Category:Topology]]
+[[Category:Homotopy theory]]
+{{Topology-stub}}