Example 3

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

Topological Vector Spaces, II, p. 54, § 7. Extremal points and extremal generators

Let $u : E \to E'$ be an affine mapping of an affine space $E$ in an affine space $E'$ ; let $C \subset E,\ C' \subset E'$ be two convex sets such that $u(C) \subset C'$ . If $x'$ is an extremal point of $C'$ and $x$ is an extremal point of $u^{-1}(x') \cap C$ , then $x$ is an extremal point of $C$ , as it follows from def. 1.

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

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