On composition of Baire functions

TL;DR

This paper investigates functions between topological spaces that preserve Baire class when composed, providing characterizations of such functions to deepen understanding of Baire function composition.

Contribution

It introduces new characterizations of functions that preserve Baire class under composition, advancing the theoretical understanding of Baire functions.

Findings

Characterizations of functions preserving Baire class under composition

Conditions under which composition with Baire class functions remains in the same class

Theoretical framework for analyzing Baire function composition

Abstract

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