Extending Baire-one functions on compact spaces

TL;DR

This paper constructs an example of a Baire-one function on a specific space that cannot be extended to its Stone-Čech compactification, addressing a question in the theory of function extension.

Contribution

It provides a counterexample demonstrating the limitations of extending Baire-one functions on certain compactifications.

Findings

Counterexample of a Baire-one function not extendable to  X

Shows limitations of extension for Baire-one functions

Addresses a question posed by Kalenda and Spurnfd

Abstract

We answer a question of O. Kalenda and J. Spurn\'{y} and give an example of a completely regular hereditarily Baire space $X$ and a Baire-one function $f:X\to [0,1]$ which can not be extended to a Baire-one function on $\beta X$.