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A remark on the uniformization in metric spaces. (English) Zbl 0959.54025
Summary: A theorem of J. Kaniewski [Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 24, 393-398 (1976; Zbl 0333.04001)] states that given a partition of a co-analytic set in a Polish space there is, under some assumptions, a co-analytic selector for this partition. We prove a similar theorem in the non-separable case. As a corollary, we obtain a simpler proof of the metric case of a uniformization theorem of C. A. Rogers and R. C. Willmott [Mathematika, London 13, Part 2, 147-150 (1966; Zbl 0171.21204)] and, using a theorem on measurable extensions of mappings, we also obtain a theorem on the uniformization of mappings, that improves a classical theorem of Kondô.

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 54C65 Selections in general topology
Citations:
Zbl 0333.04001; Zbl 0171.21204
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