Lemma 66.5.3 (040T)—The Stacks project

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Part 4: Algebraic Spaces
Chapter 66: Properties of Algebraic Spaces
Section 66.5: Quasi-compact spaces
Lemma 66.5.3 (cite)

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Lemma 66.5.3. A finite disjoint union of quasi-compact algebraic spaces is a quasi-compact algebraic space.

Proof. This is clear from Lemma 66.5.2 and the corresponding topological fact. $\square$

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