Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Varieties of Coarse Spaces

Version 1 : Received: 20 April 2018 / Approved: 23 April 2018 / Online: 23 April 2018 (12:13:38 CEST)

How to cite: Protasov, I. Varieties of Coarse Spaces. Preprints 2018, 2018040292 (doi: 10.20944/preprints201804.0292.v1). Protasov, I. Varieties of Coarse Spaces. Preprints 2018, 2018040292 (doi: 10.20944/preprints201804.0292.v1).

## 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.

## Keywords

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

## Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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