Diagonals of separately continuous functions and their analogs

Abstract

We prove that for a topological space X, an equiconnected space Z and a Baire-one mapping g:X→Z there exists a separately continuous mapping f:X2→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:X2→Z are exactly Baire-one functions, and diagonals of mappings f:X2→Z which are continuous on the first variable and Lipschitz (differentiable) on the second one, are exactly the functions of stable first Baire class.