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 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.
