Corollary
Tag 0A7Z, permanent. Cite it as [Bourbaki, Tag 0A7Z].
Lie Groups and Lie Algebras, chapter III, § 1. Lie groups
Let G be a Lie group whose topology admits a countable base and X a non-empty finite-dimensional analytic manifold with a law of analytic left operation of G on X. Suppose that G operates transitivity on X and that K is of characteristic 0. Then X is a Lie homogeneous space for G.
Let x ∈ X. The orbit of x, equal to X, is closed and we can therefore apply Proposition 14 (iii).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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