Examples are presented of Σ₁¹-universal preorders arising by requiring the existence of particular surjective functions. These are: the relation of epimorphism between countable graphs; the relation of being a continuous image (or a continuous image of some specific kind) for continua; the relation of being continuous open image for dendrites.
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The notion of a complete sequence of pairwise disjoint coanalytic sets is investigated. Several examples are given and such sequences are characterised under analytic determinacy. The ideas are based on earlier results of Saint Raymond, and generalise them.
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