Lemma 27.2.6. 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. $\square$

Comment #3196 by Dennis Keeler on

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

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