Definition 2

Tag 0BL5, permanent. Cite it as [Bourbaki, Tag 0BL5].

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 group operating on a set $X$ . $G$ is said to operate freely on $X$ if the stabilizer of every element of $X$ is $\{e\}$ , in other words if the relations $s.x = x,\ s \in G,\ x \in X$ imply $s = e$ .

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

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