Remark 2
Tag 07IZ, permanent. Cite it as [Bourbaki, Tag 07IZ].
Topological Vector Spaces, II, p. 56, § 7. Extremal points and extremal generators
If K is a compact set in a non complete Hausdorff locally convex space, and A, the closed convex envelope of K is not compact, there can be extremal points of A that do not belong to K (II, p. 87, exerc. 2).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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