Lemma 5.16.2 (053Y)—The Stacks project

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Part 1: Preliminaries
Chapter 5: Topology
Section 5.16: Constructible sets and Noetherian spaces
Lemma 5.16.2 (cite)

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Lemma 5.16.2. Let $f : X \to Y$ be a continuous map of Noetherian topological spaces. If $E \subset Y$ is constructible in $Y$, then $f^{-1}(E)$ is constructible in $X$.

Proof. Follows immediately from Lemma 5.16.1 and the definition of a continuous map. $\square$

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