Proposition 9

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

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

Let $G$ be a topological group operating continuously on a locally compact space $X$ . Then if $X/G$ is Hausdorff it is locally compact.

Since the equivalence relation on $X$ defined by $G$ is open ( $§ 2$ , no. 4, Lemma 2), the proposition results from Chapter I, $§ 10$ , no. 4, Proposition 10.

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

Cited by

Proposition 11, § 4
Proposition 13, § 4
Proposition 14, § 4

Cites

no. 4, Proposition 10