Lemma 3

Tag 01HK, permanent. Cite it as [Bourbaki, Tag 01HK].

Lie Groups and Lie Algebras, chapter IX, § 9. Compact Lie groups operating on manifolds

Let G be a compact topological group operating continuously on a topological space X; let A be a subset of X, stable under G, and W a neighbourhood of A. Then, there exists an open neighbourhood V of A stable under G and contained in $_{\circ}W$ .

Put F = X -- W and V = X-- GF. Then V is open (General Topology, Chap. III, §4, no. 1, Cor. 1 of Prop. 1), stable under G, and $A\subset V\subset W$ .

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Proposition 5, § 9
Theorem 1, § 9

Cites

General Topology, Chap. III, §4, no. 1, Cor. 1 of Prop. 1 not in this corpus