The Stacks project

Situation 81.13.2. Let $S$ be a scheme. Let $X$ be a locally Noetherian algebraic space over $S$. Let $Z \to X$ be a closed immersion and let $U \subset X$ be the complementary open subspace. Finally, let $f : X' \to X$ be a proper morphism of algebraic spaces such that $f^{-1}(U) \to U$ is an isomorphism.