Remark

Tag 0C72, permanent. Cite it as [Bourbaki, Tag 0C72].

General Topology, chapter IX, § 5. Baire spaces

The frontier of an arbitrary subset need not be nowhere dense: for example, if $A$ and $\overline{C}A$ are both dense sets, then the frontier of $A$ is the whole space.

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

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Cites

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