Lebesgue–Cech Dimensionality and Baire Classification of Vector-Valued Separately Continuous Mappings

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.