Corollary

Tag 01N5, permanent. Cite it as [Bourbaki, Tag 01N5].

Topologie algébrique, chapter I, § 2. Applications étales

Let B be a topological space. The fibre product of two étale B-spaces is an étale B-space.

Let $(E, p)$ and $(E', p')$ be étale B-spaces. The mapping pr $_1: E\times_B$ $E'\rightarrow E$ is étale (prop. 8), hence the mapping $p\circ$ pr $_1: E\times_BE'\rightarrow B$ is étale (prop. 6, a)).

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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