Corollary

Tag 0BG4, permanent. Cite it as [Bourbaki, Tag 0BG4].

General Topology, chapter II, § 4. Relations between uniform spaces and compact spaces

Let $A$ be a dense subspace of a compact space $X$ , and let $f$ be a mapping of $A$ into a complete Hausdorff uniform space $X'$ . Then $f$ can be extended by continuity to the whole of $X$ if and only if $f$ is uniformly continuous.

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

Cited by

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Cites

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