Remark 1

Tag 0C8U, permanent. Cite it as [Bourbaki, Tag 0C8U].

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

Even when $X$ and $Y$ are Polish spaces it is not in general true that the image of a Borel set in $X$ under a continuous mapping of $X$ into $Y$ is a Borel set in $Y$ (cf. Exercise 6; and no. 7, Theorem 3 Corollary).

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

Cited by

Nothing.

Cites

Exercise 6