Proposition 5

Tag 0C8K, permanent. Cite it as [Bourbaki, Tag 0C8K].

General Topology, chapter IX, § 6. Polish spaces, Souslin spaces, Borel sets

Every closed (resp. open) subspace of a Souslin space $X$ is Souslin.

For if $f$ is a continuous mapping of a Polish space $P$ onto $X$ , then the inverse image under $f$ of a closed (resp. open) subset of $X$ is a closed (resp. open) subset of $P$ , hence is a Polish subspace of $P$ (no. 1, Propositions 1 and 2).

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

Cited by

Proposition 11, § 6

Cites

Nothing.