Lemma 67.53.6 (08AK)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 67: Morphisms of Algebraic Spaces
Section 67.53: Universal homeomorphisms
Lemma 67.53.6 (cite)

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Lemma 67.53.6. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$ . The canonical closed immersion $X_{red} \to X$ (see Properties of Spaces, Definition 66.12.5) is a universal homeomorphism.

Proof. Omitted. $\square$

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