Diagonals of separately continuous functions and their analogs

摘要

We prove that for a topological space X, an equiconnected space Z and a Baire-one mapping g : X→2 there exists a separately continuous mapping f : X~2→Z with the diagonal g, i.e. g(x) = f(x,x) for every x ∈ X. Under a mild assumptions on X and Z we obtain that diagonals of separately continuous mappings f : X~2 → Z are exactly Baire-one functions, and diagonals of mappings f : X~2 →Z which are continuous on the first variable and Lipschitz (differentiable) on the second one, are exactly the functions of stable first Baire class.