Example 3

Tag 0C19, permanent. Cite it as [Bourbaki, Tag 0C19].

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

If X is any set and if g is any finite real-valued function defined on X, then the function f defined on $X \times X$ by $f(x, y) = |g(x) - g(y)|$ 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.