On asymorphisms of finitary coarse spaces

TL;DR

This paper characterizes finitary coarse spaces where every permutation acts as an asymorphism, providing insights into the structure-preserving transformations of these spaces.

Contribution

It offers a complete characterization of finitary coarse spaces with the property that all permutations are asymorphisms, a novel structural insight.

Findings

Identifies conditions under which all permutations are asymorphisms

Provides a classification of such finitary coarse spaces

Enhances understanding of symmetry in coarse geometry

Abstract

We characterize finitary coarse spaces $X$ such that every permutation of $X$ is an asymorphism.