Proposition 5

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

Topological Vector Spaces, III, p. 31, § 5. Hypocontinuous bilinear mappings

Let $u$ be a $(\mathscr{S}, \mathscr{T})$ -hypocontinuous bilinear mapping from $E \times F$ into $G$ . For every pair of sets $M \in \mathscr{S}$ , $N \in \mathscr{T}$ , $u$ is uniformly continuous on $M \times N$ .

The proposition follows immediately from prop. 2 of GT, X, § 2, No. 1 and prop. 5 of GT, X, § 2, No. 2.

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

Cited by

Nothing.

Cites

X, § 2, No. 1 not yet on this site
X, § 2, No. 2 not yet on this site