Theorem 2

Tag 0C93, permanent. Cite it as [Bourbaki, Tag 0C93].

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

Let X be a metrizable space. If we are given a sequence $(X_n)$ of mutually disjoint Souslin subspaces of X, then there exists a sequence $(B_n)$ of mutually disjoint Borel sets in X such that $X_n \subset B_n$ for each n.

The proof rests on two lemmas:

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

Cited by

Exercise 18, § 6
Lemma 5, § 6
Lemma 7, § 6
Proposition 11, § 6
Proposition 8, § 6

Cites

Nothing.