Remark 2

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

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

In a uniform space $X$ a relatively compact set $A$ is precompact, since $A$ is contained in a compact set. On the other hand, even if $X$ is Hausdorff, a precompact set need not be relatively compact in $X$ , as is shown by the case where $X$ itself is precompact but not compact.

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

Cited by

Nothing.

Cites

Nothing.