Definition 66.24.2. Let $S$ be a scheme. Let $X$ be a decent algebraic space over $S$. Let $x \in |X|$. We say that $X$ is unibranch at $x$ if the equivalent conditions of Lemma 66.24.1 hold. We say that $X$ is unibranch if $X$ is unibranch at every $x \in |X|$.
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