The Stacks project

Lemma 68.12.7. Let $S$ be a scheme. Let $X \to Y$ be a locally quasi-finite morphism of algebraic spaces over $S$. Then $\dim (X) \leq \dim (Y)$.

Proof. This follows from Lemma 68.12.6 and Properties of Spaces, Lemma 66.10.3. $\square$

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