Corollary

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

General Topology, chapter II, § 2. Uniformly continuous functions

Let $\mathfrak{U}_1$ and $\mathfrak{U}_2$ be two uniformities on a set X, and suppose that $\mathfrak{U}_1$ is finer than $\mathfrak{U}_2$ ; then the topology induced by $\mathfrak{U}_1$ is finer than the topology induced by $\mathfrak{U}_2$ .

This follows immediately from the comparison of topologies in terms of neighbourhoods (Chapter I, , no. 2, Proposition 3)

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

Cited by

Nothing.

Cites

no. 2, Proposition 3