Compactifications of metric spaces

Kocak M., Akca I.

TAIWANESE JOURNAL OF MATHEMATICS, vol.11, no.1, pp.15-26, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 1
  • Publication Date: 2007
  • Doi Number: 10.11650/twjm/1500404630
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.15-26
  • Eskisehir Osmangazi University Affiliated: No


If X is 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 (X) over tilde of a metric space in terms of the concept of near ultrafilters. We describe the topological space (X) over tilde and we investigate conditions under which (S) over tilde 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) over tilde coincides with S-LUC.