Corollary 2

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

General Topology, chapter II, § 3. Complete spaces

A filter base $\mathfrak{B}$ on a product $\prod_{i \in I} X_i$ of uniform spaces is a Cauchy filter base if and only if, for each $i \in I$ , $\operatorname{pr}_i(\mathfrak{B})$ is a Cauchy filter base on $X_i$ .

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

Cited by

Proposition 10, § 3

Cites

Nothing.