Decompositions of Borel bimeasurable mappings between complete metric spaces |
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Authors: | Petr Holický |
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Affiliation: | Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Sokolovská 83, 186 75 Prague 8, Czech Republic |
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Abstract: | We prove that every Borel bimeasurable mapping can be decomposed to a σ-discrete family of extended Borel isomorphisms and a mapping with a σ-discrete range. We get a new proof of a result containing the Purves and the Luzin-Novikov theorems as a by-product. Assuming an extra assumption on f, or that Fleissner's axiom (SCω2) holds, we characterize extended Borel bimeasurable mappings as those extended Borel measurable ones which may be decomposed to countably many extended Borel isomorphisms and a mapping with a σ-discrete range. |
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Keywords: | 54H05 54C65 54E50 |
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