# Varieties of coarse spaces

Research paper by Igor Protasov

Indexed on: 19 Mar '18Published on: 19 Mar '18Published in: arXiv - Mathematics - General Topology

#### Abstract

A class $\mathfrak{M}$ of coarse spaces is called a variety if $\mathfrak{M}$ is closed under formation of subspaces, coarse images and products. We classify the varieties of coarse spaces and, in particular, show that if a variety $\mathfrak{M}$ contains an unbounded metric space then $\mathfrak{M}$ is the variety of all coarse spaces.