Proposition 13
Tag 0C92, permanent. Cite it as [Bourbaki, Tag 0C92].
General Topology, chapter IX, § 6. Polish spaces, Souslin spaces, Borel sets
If is any Lusin (resp. Souslin) space, there exists a sieve and a continuous bijection (resp. surjection) of onto .
Referring to the definition of a Lusin space (no. 4, Definition 6) [resp. a Souslin space (no. 2, Definition 2)], we reduce to the case where
X is Polish and zero-dimensional (resp. Polish), and the preceding argument then proves the result.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.