Proposition 2

Tag 07H5, permanent. Cite it as [Bourbaki, Tag 07H5].

Topological Vector Spaces, chapter II, § 6. Weak topologies

— The weak topology $\sigma(F, G)$ is Hausdorff if and only if the duality between $F$ and $G$ is separating in $F$ .

This is a particular case of II, p. 3, 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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