Corollary 2

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

Topologie algébrique, chapter I, § 2. Applications étales

Let $p: E\rightarrow B$ be an étale and separated mapping. If the space E is connected, the group Aut $_B(E)$ operates freely on E.

In fact, if $f: E\rightarrow E$ is a B-morphism, the set of points where $f$ and Id $_E$ coincide is equal to E or to the empty set by Cor. 1.

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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