Remark 1
Tag 0B6R, permanent. Cite it as [Bourbaki, Tag 0B6R].
General Topology, chapter I, § 8. Hausdorff spaces and regular spaces
There are examples of non-Hausdorff spaces in which every point has a regular neighbourhood (Exercise 7).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
Nothing.