Corollary 2

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

Lie Groups and Lie Algebras, chapter IX, Appendix 1. Structure of compact groups

The canonical map $G\rightarrow$ lim $_{_{\leftarrow -}}G/H_{\alpha}$ is an isomorphism of topological groups. $\alpha$

Indeed, Cor. 1 implies that condition (PA) of General Topology, Chap. III, §7, no. 2, is satisfied; the assertion now follows from Prop. 2 of loc. cit.

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 2, Appendix 1

Cites

Cor. 1
General Topology, Chap. III, §7, no. 2