Example 2

Tag 07B6, permanent. Cite it as [Bourbaki, Tag 07B6].

Topological Vector Spaces, II, p. 7, § 2. Convex sets

The only non-empty convex sets in $\mathbf{R}$ are the intervals (GT, IV, § 2.4, prop. 1).

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

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Nothing.