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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 to be the inductive limit of the spheres . Then this space is weakly contractible. Since is moreover a CW-complex, it is also contractible. See Contractibility of unit sphere in Hilbert space for more.

The Long Line is an example of a space which is weakly contractible, but not contractible. This does not contradict Whitehead theorem since the Long Line does not have the homotopy type of a CW-complex. Another prominent example for this phenomenon is the Warsaw circle.

- "Homotopy type",
*Encyclopedia of Mathematics*, EMS Press, 2001 [1994]