Corollary 1

Tag 07KL, permanent. Cite it as [Bourbaki, Tag 07KL].

Topological Vector Spaces, chapter II, § 8. Complex locally convex spaces

— Let $x_0$ be a point of a complex topological vector space E and p be a continuous semi-norm in E; then there exists a continuous (complex) linear form f defined in E, such that $f(x_0) = p(x_0)$ and $|f(x)| \leq p(x)$ for all $x \in E$ .

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

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