Corollary 2

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

General Topology, chapter III, § 7. Inverse limits of topological groups and rings

If, for each $\alpha \in I$ , the group $G_\alpha$ operates transitively on the space $X_\alpha$ , and if the stabilizer of each point of $X_\alpha$ is a compact subgroup of $G_\alpha$ , then $G$ operates transitively on $X$ and the stabilizer of each point of $X$ is a compact subgroup of $G$ .

For hypothesis a) is satisfied, and $X'_\alpha = X_\alpha$ for each $\alpha$ .

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

Cited by

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Cites

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