Non-meager free sets for meager relations on Polish spaces

TL;DR

This paper proves that for any meager relation on a Polish space, there exists a large, nowhere meager subset that contains no pairs related by that relation, highlighting a significant structural property.

Contribution

It establishes the existence of large, nowhere meager E-free subsets within Polish spaces for any meager relation, advancing understanding of the structure of meager relations.

Findings

Existence of nowhere meager E-free subsets in Polish spaces for meager relations

Structural insight into meager relations on Polish spaces

Generalization of free set existence in topological spaces

Abstract

We prove that for each meager relation $E\subset X\times X$ on a Polish space $X$ there is a nowhere meager subspace $F\subset X$ which is $E$-free in the sense that $(x,y)\notin E$ for any distinct points $x,y\in F$.