Remark 4

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

Topological Vector Spaces, chapter IV, § 1. Duality

The topology $\beta(E, E')$ (IV, p. 4, def. 3) is finer than the Mackey topology. If $\beta(E, E')$ is distinct from $\tau(E, E')$ , it is not compatible with the duality between E and $E'$ . The space E is barrelled if and only if the initial topology is equal to $\beta(E, E')$ (III, p. 24).

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

Cited by

Nothing.

Cites

III, p. 24