Example 2

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

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

If G operates properly on X, then it operates properly on every subspace $X'$ of X which is a union of orbits of points of X (in other words, $X'$ is saturated with respect to the equivalence relation defined by G). For the inverse image of $X' \times X'$ in $G \times X$ is $G \times X'$ , and we can apply Proposition 3 of Chapter I, § 10, no. 1.

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

Cited by

Nothing.

Cites

Proposition 3 of Chapter I, § 10, no. 1