Remark 3

Tag 0B0H, permanent. Cite it as [Bourbaki, Tag 0B0H].

General Topology, chapter I, § 2. Continuous functions

If $f : X \to X'$ is a continuous mapping, it remains continuous if the topology of $X$ is replaced by a finer topology and the topology of $X'$ is replaced by a coarser topology (no. 1, Theorem 2). In other words, the finer the topology of $X$ and the coarser the topology of $X'$ , the more continuous mappings there are of $X$ into $X'$ .

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

Cited by

Nothing.

Cites

no. 1, Theorem 2