Corollary
Tag 0B6X, permanent. Cite it as [Bourbaki, Tag 0B6X].
General Topology, chapter I, § 8. Hausdorff spaces and regular spaces
On a regular space, every equivalence relation which is both open and closed is Hausdorff.
This follows from Proposition 14 and Proposition 8 of no. 3.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
Nothing.