The Stacks project

Lemma 67.34.7. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Assume $f$ is locally of finite type. Then there exists a canonical open subspace $X' \subset X$ such that $f|_{X'} : X' \to Y$ is locally quasi-finite, and such that the relative dimension of $f$ at any $x \in |X|$, $x \not\in |X'|$ is $\geq 1$. Formation of $X'$ commutes with arbitrary base change.

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