Almost Ultrafilters and Compactifications

Abstract

If Xis a discrete topological space, the points of its Stone-Cech compactification beta X can be regarded as ultrafilters on X, and this fact is a useful tool in analysing the properties of beta X The purpose of this paper is to describe the compactification. of X of a uniform space in terms of the concept of almost ultrafilters. We describe the topological space X* and we investigate conditions under which S* will be a semigroup compactification if S is a semigroup which has a uniform structure. These conditions will always hold if S is a topological group, and in this case our compactification S* coincides with S-LUC.