Decomposing Borel functions and structure at finite levels of the Baire hierarchy

Annals of Pure and Applied Logic 163 (12):1748-1764 (2012)
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Abstract

We prove that if f is a partial Borel function from one Polish space to another, then either f can be decomposed into countably many partial continuous functions, or else f contains the countable infinite power of a bijection that maps a convergent sequence together with its limit onto a discrete space. This is a generalization of a dichotomy discovered by Solecki for Baire class 1 functions. As an application, we provide a characterization of functions which are countable unions of continuous functions with domains of type Πn0, for a fixed n<ω. For Baire class 1 functions, this generalizes analogous characterizations proved by Jayne and Rogers for n=1 and Semmes for n=2

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References found in this work

Baire Reductions and Good Borel Reducibilities.Luca Motto Ros - 2010 - Journal of Symbolic Logic 75 (1):323-345.
Decomposing Baire Functions.J. Cichoń, M. Morayne, J. Pawlikowski & S. Solecki - 1991 - Journal of Symbolic Logic 56 (4):1273 - 1283.
A Very Discontinuous Borel Function.Juris Steprāns - 1993 - Journal of Symbolic Logic 58 (4):1268 - 1283.

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