Lemma 65.18.6. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. The functor $X_{affine, {\acute{e}tale}} \to X_{\acute{e}tale}$ is special cocontinuous and induces an equivalence of topoi from $\mathop{\mathit{Sh}}\nolimits (X_{affine, {\acute{e}tale}})$ to $\mathop{\mathit{Sh}}\nolimits (X_{\acute{e}tale})$.

**Proof.**
Omitted. Hint: compare with the proof of Topologies, Lemma 34.4.11.
$\square$

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