The Stacks project

Definition 67.9.2. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$.

  1. We say $f$ is closed if the map of topological spaces $|X| \to |Y|$ is closed.

  2. We say $f$ is universally closed if for every morphism of algebraic spaces $Z \to Y$ the morphism of topological spaces

    \[ |Z \times _ Y X| \to |Z| \]

    is closed, i.e., the base change $Z \times _ Y X \to Z$ is closed.

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View Definition 67.9.2 as pdf