Corollary 3

Tag 01P2, permanent. Cite it as [Bourbaki, Tag 01P2].

Topologie algébrique, chapter I, § 4. Revêtements

Let B be a topological space. Let E and $E'$ be locally trivial fibre B-spaces ( resp. coverings). Then $E\times_BE'$ is a locally trivial fibre B-space ( resp. a covering of B). It is trivializable if E and $E'$ are.

This follows from corollary 1, applied to the case where A, B and $B'$ are equal.

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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Cites

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