Abstract
If X is a discrete topological space, the points of its Stone-ˇCech compactification βX can be regarded as ultrafilters on X, and this fact is a useful tool in analysing the properties of βX. The purpose of this paper is to describe the compactification X of a metric space in terms of the concept of near 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 metric. These conditions will always hold if the topology of S is defined by an invariant metric, and in this case our compactification ˜ S coincides with SLUC.
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