Definition 4

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

General Topology, chapter II, § 3. Complete spaces

The complete Hausdorff uniform space $\hat{X}$ defined in the proof of Theorem 3 is called the Hausdorff completion of $X$ , and the mapping $i : X \to \hat{X}$ is called the canonical mapping of $X$ into its Hausdorff completion.

We note also the following facts:

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

Cited by

Nothing.

Cites

Theorem 3