Theorem 72.14.7. Let $S$ be a scheme. Let $X$ be a quasi-compact and quasi-separated algebraic space over $S$. Then approximation by perfect complexes holds on $X$.

**Proof.**
This follows from the induction principle of Lemma 72.9.3 and Lemmas 72.14.6 and 72.14.5.
$\square$

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