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.


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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