Corollary

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

General Topology, chapter II, § 3. Complete spaces

If $X$ is a Hausdorff uniform space, then the canonical mapping $i : X \to \hat{X}$ is an isomorphism of $X$ onto a dense subspace of $\hat{X}$ .

When $X$ is Hausdorff, $\hat{X}$ is said to be the completion of $X$ , and we generally identify $X$ with a dense subset of $\hat{X}$ by means of $i$ .

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

Cited by

Remark, § 3
Proposition 16, § 3

Cites

Nothing.