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Descriptive Set Theory is the study of definable subsets of Polish spaces, where definable is taken to mean from the Borel or projective hierarchies. Other topics include infinite games and determinacy, definable equivalence relations and Borel reductions between them, Polish groups, and effective descriptive set theory.

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In a Polish space, is every analytic set the continuous image of a Borel set from the same P...

I'm confused by a subtle point in the definition of analytic sets. Suppose I have a Polish space $X$. Now I start with the collection of Borel sets in $X$ and take all their continuous images in $X$. …