Lemma 71.6.4. Let S be a scheme. Let X be an algebraic space over S. Let D \subset X be an effective Cartier divisor. Let U = X \setminus D. Then U \to X is an affine morphism and U is scheme theoretically dense in X.
Proof. Affineness is Lemma 71.6.3. The density question is étale local on X by Morphisms of Spaces, Definition 67.17.3. Thus this follows from the case of schemes which is Divisors, Lemma 31.13.4. \square
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