Extensions of T (0)-quasi-metrics

Kunzi H. A., YILDIZ F.

ACTA MATHEMATICA HUNGARICA, vol.153, no.1, pp.196-215, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 153 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.1007/s10474-017-0753-z
  • Journal Name: ACTA MATHEMATICA HUNGARICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.196-215
  • Hacettepe University Affiliated: Yes

Abstract

Let be a partially ordered metric space, that is, a metric space (X, m) equipped with a partial order on X. We say that a T (0)-quasi-metric d on X is m-splitting provided that . Furthermore d is said to be -producing provided that d is m-splitting and the specialization partial preorder of d is equal to . It is known and easy to see that if is a partially ordered metric space that is produced by a T (0)-quasi-metric and is a total order, then there exists exactly one producing T (0)-quasi-metric on X. We first will give an example that shows that a partially ordered metric space can be uniquely produced by a T (0)-quasi-metric although is not total.