Definition 65.25.2. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. We say a point $x \in |X|$ is a *finite type point*^{1} if the equivalent conditions of Lemma 65.25.1 are satisfied. We denote $X_{\text{ft-pts}}$ the set of finite type points of $X$.

[1] This is a slight abuse of language as it would perhaps be more correct to say “locally finite type point”.

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