Ends and simple coarse structures

Abstract

This paper is devoted to introducing coarse structures in a very simple way, namely as an equivalence relation on the set of simple ends. As an application we show that Gromov boundary of every hyperbolic space is an example of a Higson corona and each Freundenthal compactification is an example of a Higson compactification.

16 pages, 4th version is significantly changed, especially Section 4. Also, a new section (Applications) added, where Mine-Yamashita-type results are proved