Remark 67.19.4. A universally injective morphism of schemes is separated, see Morphisms, Lemma 29.10.3. This is not the case for morphisms of algebraic spaces. Namely, the algebraic space X = \mathbf{A}^1_ k/\{ x \sim -x \mid x \not= 0\} constructed in Spaces, Example 65.14.1 comes equipped with a morphism X \to \mathbf{A}^1_ k which maps the point with coordinate x to the point with coordinate x^2. This is an isomorphism away from 0, and there is a unique point of X lying above 0. As X isn't separated this is a universally injective morphism of algebraic spaces which is not separated.
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Comment #210 by Rex on