A general theory for ends

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 spaces, which is a totally disconnected compact topological space. We see that the space of ends of an asymptotic resemblance space can be embedded topologically in its binary corona. We show how these two notions can be considered as generalizations of known definitions for space of ends of groups. In the end, we investigate the space of ends of groups with compatible asymptotic resemblance relations. In particular, we see that if we use our new definition, then each countable locally finite group is 0-ended, and more generally, the number of ends of each countable group is less than or equal to the supremum of the set of all number of ends of its finitely generated subgroups.