Remark

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

Topological Vector Spaces, II, p. 38, § 5. Separation of convex sets

In a Hausdorff locally convex space $E$ , let $A$ and $B$ be two closed non-empty convex sets that are disjoint, if $E$ is finite dimensional then there exists a closed hyperplane that separates $A$ from (II, p. 78, exerc. 13); but this conclusion is not necessarily true when $E$ is of infinite dimension (II, p. 78, exerc. 10 and 11).

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. 78