Definition 2

Tag 0B3C, permanent. Cite it as [Bourbaki, Tag 0B3C].

General Topology, chapter I, § 5. Open mappings and closed mappings

An equivalence relation $R$ on a topological space $X$ is said to be open (resp. closed) if the canonical mapping of $X$ onto $X/R$ is open (resp. closed).

It comes to the same thing to say that the saturation of each open (resp. closed) subset of $X$ with respect to $R$ is open (resp. closed) in $X$ (§ 3, no. 4).

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

Cited by

Nothing.

Cites

§ 3, no. 4