Proposition 4

Tag 0C8J, permanent. Cite it as [Bourbaki, Tag 0C8J].

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

Every Souslin space $X$ is of countable type.

Let $P$ be a Polish space and $f$ a continuous mapping of $P$ onto $X$ . Then the image under $f$ of a countable dense subset of $P$ is a countable dense subset of $X$ .

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

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Cites

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