Corollary

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

General Topology, chapter II, § 3. Complete spaces

If $f : X \to X'$ and $g : X' \to X''$ are two uniformly continuous mappings and $h = g \circ f$ , then $\hat{h} = \hat{g} \circ \hat{f}$ .

This is an immediate consequence of the uniqueness in Proposition 15.

(*) In other words, $i' \circ f = \hat{f} \circ i$ .

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

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