The Stacks project

Lemma 67.30.11. Let $S$ be a scheme. Let $f : X \to Y$ be a flat morphism of algebraic spaces over $S$. Let $V \to Y$ be a quasi-compact open immersion. If $V$ is scheme theoretically dense in $Y$, then $f^{-1}V$ is scheme theoretically dense in $X$.

Proof. Using the characterization of scheme theoretically dense opens in Lemma 67.17.2 and using the characterization of flat morphisms in terms of étale coverings in Lemma 67.30.5 we reduce to the case of schemes which is Morphisms, Lemma 29.25.15. $\square$

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