The Solecki dichotomy for functions with analytic graphs

TL;DR

This paper generalizes Solecki's dichotomy for Baire class 1 functions to all functions with analytic graphs, providing a proof based on elementary combinatorics and topology.

Contribution

It extends the Solecki dichotomy to functions with analytic graphs, broadening its applicability beyond Baire class 1 functions.

Findings

Dichotomy holds for all functions with analytic graphs

Provides a classical proof using elementary combinatorics and topology

Enhances understanding of function decompositions in descriptive set theory

Abstract

A dichotomy discovered by Solecki says that a Baire class 1 function from a Souslin space into a Polish space either can be decomposed into countably many continuous functions, or else contains one particular function which cannot be so decomposed. In this paper we generalize this dichotomy to arbitrary functions with analytic graphs. We provide a "classical" proof, which uses only elementary combinatorics and topology.