Lemma 65.25.3. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. We have

$X_{\text{ft-pts}} = \bigcup \nolimits _{\varphi : U \to X\text{ étale }} |\varphi |(U_0)$

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

Proof. Immediate from Lemma 65.25.1. $\square$

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