Compact-by-contractible group

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This article defines a property that can be evaluated for a topological group (usually, a T0 topological group)
View a complete list of such properties

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.

Relation with other properties

Stronger properties