Remark 1

Tag 0C1C, permanent. Cite it as [Bourbaki, Tag 0C1C].

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

If $(a_n)$ is any sequence of numbers $> 0$ and tending to 0, the $U_{a_n}$ form a fundamental system of entourages of the uniformity defined by $f$ .

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

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