Corollary 5

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

General Topology, chapter I, § 10. Proper mappings

If $X$ is any quasi-compact space and $Y$ is any topological space, then the projection $\mathrm{pr}_2 : X \times Y \to Y$ is proper.

For we may identify $Y$ with $P \times Y$ and $\mathrm{pr}_2$ with the product of $X \to P$ and $\iota_Y$ , both of which are proper mappings.

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

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