Lemma 100.9.6 (0H20)—The Stacks project

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Part 7: Algebraic Stacks
Chapter 100: Properties of Algebraic Stacks
Section 100.9: Immersions of algebraic stacks
Lemma 100.9.6 (cite)

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Lemma 100.9.6. If $f : \mathcal{X} \to \mathcal{Y}$ is an immersion, then $|f| : |\mathcal{X}| \to |\mathcal{Y}|$ is a homeomorphism onto a locally closed subset. If $f$ is a closed, resp. open immersion, then $|f|$ is closed, resp. open.

Proof. Omitted. $\square$

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