Preprint Article Version 1 This version is not peer-reviewed

# Varieties of Coarse Spaces

Version 1 : Received: 27 March 2018 / Approved: 30 March 2018 / Online: 30 March 2018 (04:49:57 CEST)

A peer-reviewed article of this Preprint also exists.

Protasov, I. Varieties of Coarse Spaces. Axioms 2018, 7, 32. Protasov, I. Varieties of Coarse Spaces. Axioms 2018, 7, 32.

Journal reference: Axioms 2018, 7, 32
DOI: 10.3390/axioms7020032

## 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.

## Subject Areas

coarse structure; coarse space; ballean; varieties of coarse spaces