Definition 64.12.1. Let $S \in \mathop{\mathrm{Ob}}\nolimits (\mathit{Sch}_{fppf})$ be a scheme. Let $F$ be an algebraic space over $S$.

A morphism of algebraic spaces over $S$ is called an

*open immersion*if it is representable, and an open immersion in the sense of Definition 64.5.1.An

*open subspace*of $F$ is a subfunctor $F' \subset F$ such that $F'$ is an algebraic space and $F' \to F$ is an open immersion.A morphism of algebraic spaces over $S$ is called a

*closed immersion*if it is representable, and a closed immersion in the sense of Definition 64.5.1.A

*closed subspace*of $F$ is a subfunctor $F' \subset F$ such that $F'$ is an algebraic space and $F' \to F$ is a closed immersion.A morphism of algebraic spaces over $S$ is called an

*immersion*if it is representable, and an immersion in the sense of Definition 64.5.1.A

*locally closed subspace*of $F$ is a subfunctor $F' \subset F$ such that $F'$ is an algebraic space and $F' \to F$ is an immersion.

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