The Stacks project

Lemma 75.7.3. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$ which is locally of finite type. Let $T' \subset T \subset |X|$ be closed subsets. If $T$ is proper over $Y$, then the same is true for $T'$.

Proof. Omitted. $\square$

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