A dichotomy for Borel functions

2008/10/08 by Marcin Sabok, Sabok, Marcin
Mathematics · #03E15 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Equations Stability Results #General Topology (math.GN) #Logic (math.LO) #Mathematical Dynamics and Fractals #math.GN #math.LO #msc:03E15

paper · pdf · doi:10.48550/arxiv.0810.1391

arxiv created 2008/10/08 · openalex publication_date 2008/10/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The dichotomy discovered by Solecki in \citeSol states that any Baire class 1 function is either σ-continuous or "includes" the Pawlikowski function P. The aim of this paper is to give an argument which is simpler than the original proof of Solecki and gives a stronger statement: a dichotomy for all Borel functions.

Related

• The Solecki dichotomy for functions with analytic graphs
• Bases for functions beyond the first Baire class
• Compact Sets of Baire Class One Functions and Maximal Almost Disjoint Families
• The Baire classification of strongly separately continuous functions on ℓ_∞
• Note on the First Part of Borel-Cantelli Lemma