The Stacks project

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

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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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