Definition 67.17.3. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $U \subset X$ be an open subspace.

The scheme theoretic image of the morphism $U \to X$ is called the

*scheme theoretic closure of $U$ in $X$*.We say $U$ is

*scheme theoretically dense in $X$*if the equivalent conditions of Lemma 67.17.2 are satisfied.

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