Remark 1
Tag 07IY, permanent. Cite it as [Bourbaki, Tag 07IY].
Topological Vector Spaces, II, p. 56, § 7. Extremal points and extremal generators
Even if the vector space E is finite dimensional the set of extremal points of a compact convex set is not necessarily closed (II, p. 89, exerc. 11).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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