Proposition 2

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

Topological Vector Spaces, chapter IV, § 2. Bidual. Reflexive spaces

— Suppose that the space $E$ is bornological or barrelled. The initial topological on $E$ is the inverse image under $c_E$ of the strong topology on $E''$ .

For, every subset of $E'$ which is strongly bounded is equicontinuous (III, p. 22, prop. 10 and 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. 22
III, p. 24