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-In [[mathematics]], a [[topological space]] is said to be '''weakly contractible''' if all of its [[homotopy group]]s are trivial.
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-==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}}

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