Lemma 28.2.6 (07ZL)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 28: Properties of Schemes
Section 28.2: Constructible sets
Lemma 28.2.6 (cite)

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Lemma 28.2.6. Let $X$ be a scheme. A subset $E$ of $X$ is retrocompact in $X$ if and only if $E \cap U$ is quasi-compact for every affine open $U$ of $X$ .

Proof. Immediate from the fact that every quasi-compact open of $X$ is a finite union of affine opens. $\square$

Comments (2)

Comment #3196 by Dennis Keeler on February 11, 2018 at 18:14

I believe that $Z=E$ is intended here.

Comment #3301 by Johan on May 17, 2018 at 15:20

Thanks, fixed here.

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