In this paper, we study properties of asymptotic resemblance relations induced by
compatible coarse structures on groups. We generalize the notion of asymptotic …

To a metric space X we associate a compact topological space\(\nu'({X})\) called the corona
of X. Then a coarse map\(f: X\rightarrow Y\) between metric spaces is mapped to a …

We introduce the notion of large scale dimensiongrad as a large scale invariant of
asymptotic resemblance spaces. Consequently it can be considered as a large scale …

In this paper, we suggest a definition for the space ends of asymptotic resemblance spaces
(or coarse spaces). Besides, we introduce the binary corona of asymptotic resemblance …

This paper studies coarse compactifications and their boundary. We introduce two
alternative descriptions to Roe's original definition of coarse compactification. One approach …

We define the concept of small subsets of asymptotic resemblance spaces and obtain some
of their properties. In addition, we show that if the ideal of all small subsets of a metric space …