Proposition 2
Tag 07QT, permanent. Cite it as [Bourbaki, Tag 07QT].
Topological Vector Spaces, chapter IV, § 1. Duality
Let E be a locally convex space, and let A be a convex subset of E (for example, a vector subspace of E). The closure of A is the same for the initial topology and for the weakened topology of E.
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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