Compactifications of metric spaces


Kocak M., Akca I.

TAIWANESE JOURNAL OF MATHEMATICS, cilt.11, sa.1, ss.15-26, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 1
  • Basım Tarihi: 2007
  • Doi Numarası: 10.11650/twjm/1500404630
  • Dergi Adı: TAIWANESE JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.15-26
  • Eskişehir Osmangazi Üniversitesi Adresli: Hayır

Özet

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.