Example 3

Tag 0B35, permanent. Cite it as [Bourbaki, Tag 0B35].

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

Let $f$ be a surjection of a set $X$ onto a topological space $X'$ ; if we give $X$ the topology which is the inverse image under $f$ of the topology of $X'$ (§ 2, no. 3, Example 1), then $f$ is continuous, open and closed.

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

Cited by

Example, § 10

Cites

§ 2, no. 3, Example 1