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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