Bourbaki

Remark 2

Tag 0B0G, permanent. Cite it as [Bourbaki, Tag 0B0G].

General Topology, chapter I, § 2. Continuous functions

The finer the topology, the more open sets, closed sets and neighbourhoods; the finer the topology, the smaller (resp. the larger) the closure (resp. the interior) of a set; the finer the topology, the fewer dense sets.

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

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Transcribed from the printed volume. Not translated.