Remark

Tag 0BA8, permanent. Cite it as [Bourbaki, Tag 0BA8].

General Topology, chapter I, § 10. Proper mappings

If $X'$ is not Hausdorff it can happen that $g \circ f$ is proper and $f$ not; for example, take $X$ and $X''$ to consist of one point and $X'$ to consist of two points, with the coarsest topology.

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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