Corollary 3
Tag 07KN, permanent. Cite it as [Bourbaki, Tag 07KN].
Topological Vector Spaces, chapter II, § 8. Complex locally convex spaces
— Let M be a finite dimensional vector subspace of a Hausdorff complex locally convex space E. Then there exists a closed vector subspace N of E that is a topological complement of M in E.
The proofs using theorem 1, p. 24 are the same as those of II, p. 23, cor. 2 and cor. 3, p. 24, prop. 2 and p. 25, cor. 2.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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