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The Stacks project

Definition 67.27.1. Let S be a scheme. Let f : X \to Y be a morphism of algebraic spaces over S.

  1. We say f is locally quasi-finite if the equivalent conditions of Lemma 67.22.1 hold with \mathcal{P} = \text{locally quasi-finite}.

  2. Let x \in |X|. We say f is quasi-finite at x if there exists an open neighbourhood X' \subset X of x such that f|_{X'} : X' \to Y is locally quasi-finite.

  3. A morphism of algebraic spaces f : X \to Y is quasi-finite if it is locally quasi-finite and quasi-compact.


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