Corollary 1

Tag 079G, permanent. Cite it as [Bourbaki, Tag 079G].

Topological Vector Spaces, I, p. 14, § 2. Linear varieties in a topological vector space

In a Hausdorff topological vector space $E$ over a complete non-discrete valued division ring $K$ , every vector subspace $F$ of finite dimension is closed in $E$ . For, if $F$ is of dimension $n$ then it is isomorphic to $K_s^n$ ; it is therefore complete and hence closed in $E$ (GT, II, § 3.4, prop. 8).

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

Cited by

Nothing.

Cites

II, § 3