Corollary

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

General Topology, chapter X, § 3. Special function spaces

Let $X$ be a uniform space and let $H$ be an equicontinuous group of homeomorphisms of $X$ onto itself. Then the topology of pointwise convergence in $X$ is compatible with the group structure of $H$ .

This is a consequence of Proposition 10, together with § 2, no. 1, Proposition 1, Corollary 5.

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

Cited by

Exercise 19, § 3

Cites

§ 2, no. 1, Proposition 1
Corollary 5
Proposition 10