Corollary 2

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

General Topology, chapter I, § 10. Proper mappings

Every continuous mapping $f$ of a quasi-compact space $X$ into a Hausdorff space $Y$ is proper.

The composition $X \xrightarrow{f} Y \to P$ is proper by Corollary 1; hence $f$ is proper by no. 1, Proposition 5 d). Alternatively we may apply the criterion b) of Theorem 1, using § 9, no. 4, Theorem 2, Corollary 2.

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

Cited by

Proposition 7, § 10
Remark 1, § 2

Cites

Corollary 1
no. 1, Proposition 5
Theorem 1
§ 9, no. 4, Theorem 2
Corollary 2