Lemma 87.17.5. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of formal algebraic spaces over $S$ which is representable by algebraic spaces. Then $f$ is quasi-compact in the sense of Definition 87.17.4 if and only if $f$ is quasi-compact in the sense of Bootstrap, Definition 80.4.1.

**Proof.**
This is immediate from the definitions and Lemma 87.17.3.
$\square$

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