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 formula_1 to be the inductive limit of the spheres formula_2. Then this space is weakly contractible. Since formula_1 is moreover a CW-complex, it is also contractible. See Contractibility of unit sphere in Hilbert space for more.