The Stacks project

Remark 66.15.4. Lemma 66.15.3 holds for decent algebraic spaces, see Decent Spaces, Lemma 68.12.8. In fact a decent algebraic space with one point is a scheme, see Decent Spaces, Lemma 68.14.2. This also holds when $X$ is locally separated, because a locally separated algebraic space is decent, see Decent Spaces, Lemma 68.15.2.