Compact-by-contractible group

Definition
A topological group is termed compact-by-contractible if it has a closed compact subgroup such that the quotient space is contractible.

In the particular case where the quotient space is also paracompact Hausdorff, the compact subgroup is a topological factor, and the projection onto this factor is a strong deformation retraction. This follows from the fact that the vector bundle class functor is homotopy-invariant for paracompact Hausdorff spaces.

Stronger properties

 * Topological space with contractible normal and compact retract