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 , 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.
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Cites
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