Remark 4

Tag 0CAX, permanent. Cite it as [Bourbaki, Tag 0CAX].

General Topology, chapter X, § 1. The uniformity of $\mathscr{G}$-convergence

Let $H$ be a subset of $\mathscr{F}(X; Y)$ . By abuse of language, the uniformity (resp. topology) induced on $H$ by the uniformity (resp. topology) of $\mathscr{S}$ -convergence on $\mathscr{F}(X; Y)$ is called the uniformity (resp. topology) of $\mathscr{S}$ -convergence on the set $H$ .

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

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