Abstract
We solve the problem of the construction of separately continuous functions on a product of two topological spaces with given restriction. It is shown, in particular, that, for an arbitrary topological space X and a function g: X → R of the first Baire class, there exists a separately continuous function f: X × X → R such that f(x, x) = g(x) for every x ∈ X.
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Mykhailyuk, V.V. Construction of Separately Continuous Functions with Given Restriction. Ukrainian Mathematical Journal 55, 866–872 (2003). https://doi.org/10.1023/B:UKMA.0000010263.26005.80
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DOI: https://doi.org/10.1023/B:UKMA.0000010263.26005.80