Definition 64.7.5. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $x \in |X|$. Let $\mathcal{P}$ be a property of germs of schemes which is étale local. We say $X$ has property $\mathcal{P}$ at $x$ if any of the equivalent conditions of Lemma 64.7.4 hold.

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