Duality between measure and category in uncountable locally compact abelian Polish groups

TL;DR

This paper proves that uncountable locally compact abelian Polish groups do not admit addition-preserving Erdős-Sierpiński mappings, extending previous results in the field.

Contribution

It generalizes earlier findings by showing the non-existence of such mappings in a broader class of groups.

Findings

No addition-preserving Erdős-Sierpiński mapping exists in uncountable locally compact abelian Polish groups.

The result extends previous work by Bartoszyński and Kysiak.

The paper establishes a fundamental limitation in the measure-category duality for these groups.

Abstract

We show that there is no addition preserving Erd\H{o}s-Sierpi\'nski mapping on any uncountable locally compact abelian Polish group. This generalizes results of Bartoszy\'nski and Kysiak.