Definition 2
Tag 0B6O, permanent. Cite it as [Bourbaki, Tag 0B6O].
General Topology, chapter I, § 8. Hausdorff spaces and regular spaces
A topological space is said to be regular if it is Hausdorff and satisfies axiom (O_{III}); its topology is then said to be regular.
A discrete space is regular. \* We shall see in § 9 that every locally compact space (in particular the real line ) is regular. \*
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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