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Applications of Luzinian separation principles (non-separable case). (English) Zbl 0543.54035

The concept of Baire sets in non-separable spaces is introduced and the connections with the concepts of non-separable analytic and Luzin spaces introduced in former papers of the authors is investigated. The Luzin first separation principle is generalized and used to characterize several types of analytic and Luzin spaces. The measurable images of analytic sets are studied and bimeasurable mappings are characterized. These applications of the Luzin principle suppose some property of preserving of the discreteness for the measurable mappings involved. It would be interesting to weaken this assumption as much as possible.

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
54C50 Topology of special sets defined by functions
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