Corollary 1

Tag 0BA9, permanent. Cite it as [Bourbaki, Tag 0BA9].

General Topology, chapter I, § 10. Proper mappings

If $f : X \to Y$ is a proper mapping, then the restriction of $f$ to a closed subset $F$ of $X$ is a proper mapping of $F$ into $Y$ .

For this restriction is the composition $f \circ j$ , where $j : F \to X$ is the canonical injection, which is proper by Proposition 2.

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

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