Corollary 2

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

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

Let $K$ be a complete non-discrete valued division ring, and $E$ be a Hausdorff topological vector space of finite dimension over $K$ . If $F$ is any topological vector space over $K$ , then every linear mapping of $E$ in $F$ is continuous.

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

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Cites

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