Corollary 1

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

Lie Groups and Lie Algebras, chapter III, § 10. The automorphism group of a Lie group

Let G be a finite-dimensional real Lie group and $G_0$ its identity component. Suppose that G is generated by $G_0$ and a finite number of elements. Then Aut G has the topology $\mathscr{T}_\beta$ and is a finite-dimensional real Lie group.

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

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Cites

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