Corollary

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

Topological Vector Spaces, II, p. 55, § 7. Extremal points and extremal generators

Let A be a compact convex set in a Hausdorff locally convex space E. Then every closed support hyperplane H of A contains at least one extremal point of A.

For, if $f(x) = \alpha$ is an equation of H and $f(x) \leq \alpha$ in A, it is sufficient to apply prop. 1 to $f$ .

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

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