Abstract
For a metrizable space X with finite Lebesgue–Cech dimensionality, a topological space Y, and a topological vector space Z, we consider mappings f: X × Y → Z continuous in the first variable and belonging to the Baire class α in the second variable for all values of the first variable from a certain set everywhere dense in X. We prove that every mapping of this type belongs to the Baire class α + 1.
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Kalancha, A.K., Maslyuchenko, V.K. Lebesgue–Cech Dimensionality and Baire Classification of Vector-Valued Separately Continuous Mappings. Ukrainian Mathematical Journal 55, 1894–1898 (2003). https://doi.org/10.1023/B:UKMA.0000027049.00915.69
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DOI: https://doi.org/10.1023/B:UKMA.0000027049.00915.69