Selectors and orderings of coarse spaces

TL;DR

This paper investigates how linear orders compatible with coarse structures influence macro-uniform selectors in coarse spaces, revealing new relationships between orderings and coarse geometric properties.

Contribution

It introduces the concept of compatible linear orders on coarse spaces and explores their interplay with macro-uniform selectors, advancing understanding of coarse geometric structures.

Findings

Established conditions for linear orders to be compatible with coarse structures

Demonstrated how compatible orders affect macro-uniform selectors

Provided new insights into the structure of coarse spaces

Abstract

Given a coarse space $(X, \mathcal{E})$, we consider linear orders on $X$ compatible with the coarse structure $\mathcal E$ and explore interplays between these orders and macro-uniform selectors of $(X, \mathcal{E})$.