The analytic sets are the continuous images of the closed sets, and this is easily shown to be equivalent to projections of trees on ω×ω. We will briefly introduce their effective analogue and characterize these as the projections of computable trees on ω×ω. The Gandy-Harrington topology is generated by taking these new sets as a basis. We will prove a couple facts about this topology that are useful in the study of equivalence relations. In particular, we show that the G-H topology is strong Choquet and that A×B is G-H comeager in X×X whenever A and B are G-H comeager in X.
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