Definition 66.17.3. 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 66.17.2 are satisfied.