On Baire classification of mappings with values in connected spaces

TL;DR

This paper extends the Lebesgue-Hausdorff Theorem to characterize Baire-one functions for a broader class of mappings on arbitrary topological spaces, focusing on those with values in connected spaces.

Contribution

It generalizes the classical theorem to include $\sigma$-strongly functionally discrete mappings on arbitrary topological spaces.

Findings

Extended the characterization of Baire-one functions

Applied to mappings with values in connected spaces

Broadened the scope of the Lebesgue-Hausdorff Theorem

Abstract

We generalize the Lebesgue-Hausdorff Theorem on the characterization of Baire-one functions for $\sigma$-strongly functionally discrete mappings defined on arbitrary topological spaces