Bourbaki

Remark

Tag 07C7, permanent. Cite it as [Bourbaki, Tag 07C7].

Topological Vector Spaces, II, p. 15, § 2. Convex sets

In a topological vector space E, every convex set C is connected. In fact, if a∈Ca \in C, then C is a union of segments with end point a and closed at a; these are connected and the result follows from GT, I, § 11.1, prop. 2.

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

Cited by

Nothing.

Cites

Nothing.

Transcribed from the printed volume. Not translated.