Proposition 1

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

General Topology, chapter II, § 3. Complete spaces

In a uniform space $X$ , if two sets $A$ and $B$ are $V$ -small and intersect, then their union $A \cup B$ is $\vec{V}$ -small.

Let $x$ and $y$ be any two points of $A \cup B$ , and let $Z \in A \cap B$ . Then $(x, z) \in V$ and $(z, y) \in V$ , so that $(x, y) \in \overline{V}$ .

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

Cited by

Theorem 3, § 3

Cites

Nothing.