Definition 67.53.2. Let $S$ be a scheme. A morphism $f : X \to Y$ of algebraic spaces over $S$ is called a *universal homeomorphism* if and only if for every morphism of algebraic spaces $Z \to Y$ the base change $Z \times _ Y X \to Z$ induces a homeomorphism $|Z \times _ Y X| \to |Z|$.

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