No abstract

We generalize the Lebesgue-Hausdorff Theorem on the characterization of Baire-one functions for σ-strongly functionally discrete mappings defined on arbitrary topological spaces.1991 Mathematics Subject Classification. Primary 54C08, 26A21; Secondary 54C50, 54H05.

We study the maps between topological spaces whose composition with Baire class α maps also belongs to the α'th Baire class and give characterizations of such maps.

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 :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.

We present σ-strongly functionally discrete mappings which expand the class of σ-discrete mappings and generalize Banach's theorem on analytically representable functions.