Corollary

Tag 04UX, permanent. Cite it as [Bourbaki, Tag 04UX].

Commutative Algebra, chapter VI, § 5. The topology defined by a valuation

Suppose that $v$ is not improper and $K$ is complete. Let $E$ be a Hausdorff topological vector space over $K$ and $F$ a finite-dimensional vector subspace of $E$ . Then $F$ is closed.

$F$ is complete.

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

Cited by

Proposition 11, § 8
Proposition 2, § 8

Cites

Nothing.