Definition 65.12.5. Let $S$ be a scheme, and let $X$ be an algebraic space over $S$. Let $Z \subset |X|$ be a closed subset. An *algebraic space structure on $Z$* is given by a closed subspace $Z'$ of $X$ with $|Z'|$ equal to $Z$. The *reduced induced algebraic space structure* on $Z$ is the one constructed in Lemma 65.12.3. The *reduction $X_{red}$ of $X$* is the reduced induced algebraic space structure on $|X|$.

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