Construction of Separately Continuous Functions with Given Restriction
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.
English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 5, pp 866-872.
Citation Example: Mykhailyuk V. V. Construction of Separately Continuous Functions with Given Restriction // Ukr. Mat. Zh. - 2003. - 55, № 5. - pp. 716-721.