Difference between revisions of "Compact-by-contractible group"

From Groupprops
Jump to: navigation, search
m (1 revision)
(No difference)

Latest revision as of 23:19, 7 May 2008

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


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