Construction of Separately Continuous Functions with Given Restriction
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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.
KeywordsContinuous Function Topological Space Baire Class Arbitrary Topological Space Separately Continuous Function
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