Remark

Tag 0BL3, permanent. Cite it as [Bourbaki, Tag 0BL3].

General Topology, chapter III, § 4. Groups operating properly on a topological space; compact ness in topological groups and spaces with operators

Proposition 4 shows that if a topological group $G$ operates properly on a homogeneous space $G/H$ , then the subgroup $H$ is quasi-compact (and therefore compact if $G$ is Hausdorff). It can be shown that this is also a sufficient condition for $G$ to operate properly on $G/H$ (Exercise 3).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Exercise 3
Proposition 4