Corollary 2

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

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

If K is a quasi-compact subgroup of a topological group G, then the equivalence relation $x^{-1}y \in K$ is closed, and the canonical mapping $\varphi : G \to G/K$ is proper.

The first assertion follows from Corollary 1 applied to G acting by right translations on itself, and the second assertion then follows from Chapter I, , no. 2, Theorem 1

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

Cited by

Corollary 3, § 4

Cites

Corollary 1
no. 2, Theorem 1