Proposition 6

Tag 0B89, permanent. Cite it as [Bourbaki, Tag 0B89].

If $X$ is a Hausdorff space, a subset $A$ of $X$ is relatively compact if and only if $\overline{A}$ is compact.

If $A$ is relatively compact, then $\overline{A}$ is compact by Proposition 4 and its corollary; the reverse implication is self-evident.

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

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