Equiconnected spaces and Baire classification of separately continuous functions and their analogs

TL;DR

This paper studies the Baire classification of functions defined on product spaces, focusing on mappings that are continuous in one variable and have Baire class properties in the other, within a broad class of spaces including metrizable ones.

Contribution

It extends the understanding of Baire classification for separately continuous functions to a wide class of spaces and introduces new results for functions into equiconnected spaces.

Findings

Characterization of Baire class functions in equiconnected spaces

Extension of Baire classification results to metrizable and related spaces

Identification of conditions for separate continuity and Baire class properties

Abstract

We investigate the Baire classification of mappings $f:X\times Y\to Z$, where $X$ belongs to a wide class of spaces, which includes all metrizable spaces, $Y$ is a topological space, $Z$ is an equiconnected space, which are continuous in the first variable and for a dense set in $X$ these mappings are functions of a Baire class $\alpha$ in the second variable.