Corollary
Tag 07RI, permanent. Cite it as [Bourbaki, Tag 07RI].
Topological Vector Spaces, chapter IV, § 1. Duality
— Every product of barrelled spaces is barrelled.
A locally convex space is barrelled if and only if the initial topology is identical with (IV, p. 4, Remark 3). Hence it is enough to apply prop. 15 (iv).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
Nothing.