Corollary 1

Tag 0AI3, permanent. Cite it as [Bourbaki, Tag 0AI3].

Lie Groups and Lie Algebras, chapter III, § 8. Lie groups over R or Qp

Let $G$ be a topological group. There exists on $G$ at most one analytic manifold structure over $\mathbf{R}$ (resp. $\mathbf{Q}_p$ ) compatible with the topological group structure on $G$ .

This follows immediately from Theorem 1.

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

Cited by

Exercise 6, § 8

Cites

Theorem 1