Corollary 3
Tag 01IL, permanent. Cite it as [Bourbaki, Tag 01IL].
Lie Groups and Lie Algebras, chapter IX, Appendix 1. Structure of compact groups
G is a Lie group if and only if there exists a neighbourhood of the identity element of G that contains no normal subgroup distinct from .
The necessity of this condition has already been proved (Chap. III, §4, no. 2, Cor. 1 of Th. 2), and the sufficiency is an immediate consequence of Cor. 1.
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
Nothing.
Cites
- Chap. III, §4, no. 2, Cor. 1 of Th. 2 not in this corpus
- Cor. 1