Corollary

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

Topological Vector Spaces, chapter II, § 2. Convex sets

— In the space $\mathbf{R}^n$ every parallelootope (GT, VI, § 1.3) is a convex subset.

For it is the image under an affine linear mapping of a rectangular parallelepiped, and this last is convex by prop. 6.

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

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Nothing.