Abstract
We introduce balleans as asymptotical counterparts of uniform topological spaces. Using slowly oscillating functions, for every ballean we define two compact spaces: corona and binary corona. These spaces can be considered as generalizations of the Higson's coronas of metric spaces and the spaces of ends of groups, respectively. We consider some balleans related to an infinite group and prove some results concerning their coronas. At the end we apply these results to describe the compact right-zero semigroups which are continuous homomorphic images of G * , the reminder of the Stone–Čech compactification of discrete group G.
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