COMPACTIFICATIONS OF METRIC SPACES

If X is a discrete topological space, the points of its Stone-Čech 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...

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Bibliographic Details
Published in:Taiwanese journal of mathematics 2007-03, Vol.11 (1), p.15-26
Main Authors: Koçak, M., Akça, İ.
Format: Article
Language:English
Subjects:
Compactification
Continuous functions
Mathematical theorems
Metric spaces
Semigroups
Topological compactness
Topological spaces
Topological theorems
Topology
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Summary:If X is a discrete topological space, the points of its Stone-Čech 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 S̃ 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 S̃ coincides with SLUC
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500404630