Corollary

Tag 0B1E, permanent. Cite it as [Bourbaki, Tag 0B1E].

Let $f : X \to X'$ be a continuous map and $L'$ a locally closed subset of $X'$ ; then $f^{-1}(L')$ is locally closed in $X$ .

This follows immediately from Proposition 5 above and Theorem 1 of § 2, no. 1.

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

Cited by

Nothing.