Lemma 5.15.11 (09YI)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 5: Topology
Section 5.15: Constructible sets
Lemma 5.15.11 (cite)

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Lemma 5.15.11. Let $X$ be a topological space. Assume $X$ has a basis consisting of quasi-compact opens. For $E, E'$ constructible in $X$ , the intersection $E \cap E'$ is constructible in $E$ .

Proof. Combine Lemmas 5.15.8 and 5.15.10. $\square$

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