The question is stated in the title. I think BCnrd states in a comment here


[Is every (Artin/DM) algebraic stack fibered in sets an algebraic space?](https://mathoverflow.net/questions/41833/is-every-artin-dm-algebraic-stack-fibered-in-sets-an-algebraic-space)


that while the answer is not found in Laumon & Moret-Bailly, but that it is nevertheless true. Does anyone know of a reference? (Also: I only care about stacks over $\mathbb{C}$, if that makes a difference.)



Reference request: an algebraic stack whose closed points have no automorphisms is an algebraic space
In case you're still looking for a reference I Lemma 2.3.9 of Abramovich and Hassett stable varieties with a twist should do it (consider the map to a point, which has no automorphisms, which by assumptions is injective on automorphism groups)


<http://arxiv.org/pdf/0904.2797v1.pdf>


