Lemma 29.16.4. Let $S$ be a scheme. We have

$S_{\text{ft-pts}} = \bigcup \nolimits _{U \subset S\text{ open}} U_0$

where $U_0$ is the set of closed points of $U$. Here we may let $U$ range over all opens or over all affine opens of $S$.

Proof. Immediate from Lemma 29.16.1. $\square$

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