Example 1

Tag 0C6Z, permanent. Cite it as [Bourbaki, Tag 0C6Z].

General Topology, chapter IX, § 5. Baire spaces

The empty subset of $X$ is nowhere dense. In a Hausdorff space $X$ , a set consisting of a single point is nowhere dense if and only if the point is not isolated in $X$ . A dense subset is never nowhere dense (unless $X = \emptyset$ ).

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

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