Definition 5

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

General Topology, chapter II, § 3. Complete spaces

The Hausdorff uniform space $i(X)$ defined in the proof of Theorem 3 is called the Hausdorff uniform space associated with $X$ .

The Hausdorff completion of $X$ is thus the completion of the Hausdorff uniform space associated with $X$ .

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

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