Remarks

Tag 0E95, permanent. Cite it as [Bourbaki, Tag 0E95].

General Topology, chapter I, § 2. Continuous functions

1) Let $\mathfrak{B}$ be a base (§ 1, no. 3) of the topology of $X'$ ; then for $f : X \to X'$ to be continuous, it is necessary and sufficient that $\overline{f^{-1}(U')}$ is open in $X$ for every $U' \in \mathfrak{B}$ .

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

Cited by

Nothing.

Cites

§ 1, no. 3