Corollary

Tag 01M9, permanent. Cite it as [Bourbaki, Tag 01M9].

Topologie algébrique, chapter I, § 1. Produits fibrés et carrés cartésiens

Let X and Y be topological spaces and let $f: X\rightarrow$ Y be a continuous mapping. Let T be a locally compact topological space. If the mapping $f$ is strict, the same is true of the mapping $f\times$ Id $_T$ of $X\times T$ into $Y\times T$ .

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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