Lattices of coarse structures

TL;DR

This paper explores the lattice of coarse structures on a set, focusing on properties like metrizability, local finiteness, and cellularity, providing a lattice-theoretic perspective.

Contribution

It introduces a lattice-theoretic analysis of various classes of coarse structures, including metrizable, locally finite, and cellular structures.

Findings

Characterization of metrizable coarse structures

Analysis of locally finite coarse structures

Study of cellular coarse structures

Abstract

We consider the lattice of coarse structures on a set $X$ and study metrizable, locally finite and cellular coarse structures on $X$ from the lattice point of view.