Remark 3

Tag 07G3, permanent. Cite it as [Bourbaki, Tag 07G3].

Topological Vector Spaces, II, p. 40, § 5. Separation of convex sets

The restriction to $X$ of a continuous affine function in $E$ is a function that is affine in $X$ (i.e. both concave and convex II, p. 17); but it may be the case that there exist continuous affine functions in a compact convex set $X \subset E$ , that are not the restrictions to $X$ of continuous affine functions in $E$ (II, p. 78, exerc. II, c)). However :

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

Cited by

Nothing.

Cites

II, p. 17
II, p. 78