Corollary

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

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

Let $E$ be a left topological vectorspace over $K$ , $H$ a closed hyperplane of $E$ and $D$ a 1-dimensional vector subspace of $E$ an algebraic supplement of $H$ . Suppose that $v$ is not improper. Then $D$ is a topological supplement of $H$ .

Taking account of Propositions 1 and 3, the proof is the same as that of Topological Vector Spaces, Chapter I, § 2, Corollary 2 to Theorem 1.

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

Cited by

Nothing.

Cites

Topological Vector Spaces, Chapter I, § 2, Corollary 2 to Theorem 1 not yet on this site: EVT I