Example 2

Tag 0C18, permanent. Cite it as [Bourbaki, Tag 0C18].

General Topology, chapter IX, § 1. Generation of a uniformity by a family of pseudometrics; uniformizable spaces

If X is any set, the function f defined on $X \times X$ by the conditions $f(x, x) = 0$ for all $x \in X, f(x, y) = +\infty$ if $x \neq y$ is a pseudometric on X.

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

Cited by

Example 4, § 1

Cites

Nothing.