## 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
Full Text: