Definition 1

Tag 0B32, permanent. Cite it as [Bourbaki, Tag 0B32].

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

Let $X, X'$ be two topological spaces. A mapping $f : X \to X'$ is open (resp. closed) if the image under $f$ of each open (resp. closed) set of $X$ is open (resp. closed) in $X'$ .

In particular, $f(X)$ is then an open (resp. closed) subset of $X'$ .

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

Cited by

Proposition 1, § 5

Cites

Nothing.