## 66.18 Dominant morphisms

We copy the definition of a dominant morphism of schemes to get the notion of a dominant morphism of algebraic spaces. We caution the reader that this definition is not well behaved unless the morphism is quasi-compact and the algebraic spaces satisfy some separation axioms.

Definition 66.18.1. Let $S$ be a scheme. A morphism $f : X \to Y$ of algebraic spaces over $S$ is called dominant if the image of $|f| : |X| \to |Y|$ is dense in $|Y|$.

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