Corollary 1

Tag 078H, permanent. Cite it as [Bourbaki, Tag 078H].

Topological Vector Spaces, chapter I, § 1. Topological vector spaces

Let G be a topological vector space on K. In order that a set H of mappings of G in E be equicontinuous, it is necessary and sufficient that, for all $i \in I$ , the set $f_i \circ u$ where u varies in H should be equicontinuous.

This is a particular case of GT, X, § 2.2, prop. 3.

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

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Cites

X, § 2 not yet on this site