Preprint Article Version 1 This version is not peer-reviewed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)

How to cite: Protasov, I. Varieties of Coarse Spaces. Preprints 2018, 2018030254 (doi: 10.20944/preprints201803.0254.v1). Protasov, I. Varieties of Coarse Spaces. Preprints 2018, 2018030254 (doi: 10.20944/preprints201803.0254.v1).

Abstract

A class M of coarse spaces is called a variety if 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 M contains an unbounded metric space then M is the variety of all coarse spaces.

Subject Areas

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

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