Extension of continuous functions to Baire-one functions

TL;DR

This paper explores the extension of continuous functions to Baire-one functions by introducing the concept of B_1-retracts and examining their relationship with H_1-retracts.

Contribution

It introduces the notion of B_1-retracts and analyzes their connection to H_1-retracts, advancing the understanding of function extension in topology.

Findings

Defined B_1-retracts and studied their properties

Established relationships between B_1- and H_1-retracts

Provided new insights into function extension mechanisms

Abstract

We introduce the notion of $B_1$-retract and investigate the connection between $B_1$- and $H_1$-retracts.