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On projection of nonseparable Souslin and Borel sets along separable spaces. (English) Zbl 1007.54035

The authors use the method of reducing a space to a separable space by a measurable function. They prove some results on descriptive properties of subsets of product spaces \(X\times Y\) by reduction to known separable analogues. Namely, they generalize theorems on generalized projections \(\{x\in X:\{y\in Y:(x,y)\in S\}\in\mathcal D\}\) where \(\mathcal D\) is a family of sets that are small in some sense, and theorems on bimeasurability, and on uniformization.

MSC:

54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
03E15 Descriptive set theory
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