# Lexicographic products as compact spaces of the first Baire clas

## TL;DR

This paper explores how lexicographic products can construct compact spaces of first Baire class functions that are not representable as spaces with countably many discontinuities, highlighting limitations in function space representations.

## Contribution

It introduces a novel use of lexicographic products to generate examples of compact first Baire class function spaces with unique properties.

## Key findings

- Lexicographic products produce new compact spaces of first Baire class functions.
- Some constructed spaces cannot be represented as functions with countably many discontinuities.
- The results reveal limitations in existing function space representations.

## Abstract

We use lexicographic products to give examples of compact spaces of first Baire class functions on a compact metric space that cannot be represented as spaces of functions with countably many discontinuities.