Lemma 66.22.2. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$ which are decent and have finitely many irreducible components. If $f$ is birational then $f$ is dominant.

**Proof.**
Follows immediately from the definitions. See Morphisms of Spaces, Definition 65.18.1.
$\square$

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