Lemma 71.6.3. Let S be a scheme. Let X be an algebraic space over S. Let Z \subset X be a locally principal closed subspace. Let U = X \setminus Z. Then U \to X is an affine morphism.
Proof. The question is étale local on X, see Morphisms of Spaces, Lemmas 67.20.3 and Lemma 71.6.2. Thus this follows from the case of schemes which is Divisors, Lemma 31.13.3. \square
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