How can we recover Baire class one functions?

TL;DR

This paper characterizes Baire class one functions between separable metrizable spaces and explores how they can be reconstructed from limited data, linking this to dual space separability in Banach spaces.

Contribution

It provides a characterization of Baire class one functions based on recoverability from small sets and connects this to the separability of dual Banach spaces.

Findings

Baire class one functions can be recovered from small sets using a simple algorithm

A new characterization of Baire class one functions is established

The work links function recoverability to dual space separability in Banach spaces

Abstract

Let X and Y be separable metrizable spaces, and f:X-->Y be a function. We want to recover f from its values on a small set via a simple algorithm. We show that this is possible if f is Baire class one, and in fact we get a characterization. This leads us to the study of sets of Baire class one functions and to a characterization of the separability of the dual space of an arbitrary Banach space.