A weight-free characterisation of Yu's Property A

TL;DR

This paper proves that for any discrete metric space with bounded geometry, the generalized F ext{"o}lner sets exhibiting Yu's Property A can always be chosen as subsets of the space itself, providing a complete characterization.

Contribution

It establishes a necessary and sufficient condition for selecting F ext{"o}lner sets as subsets of the space in the context of Yu's Property A.

Findings

F ext{"o}lner sets can be chosen as subsets of the space for spaces with bounded geometry.

Provides a complete characterization of when this selection is possible.

Clarifies the structure of spaces with Yu's Property A.

Abstract

In this short note, we give a complete answer to the question of when the generalised F\o lner sets exhibiting property A can be chosen to be subsets of the space itself. More precisely, we prove that this holds for any discrete metric space of bounded geometry.