Certain observations on antisymmetric T0-quasi-metric spaces

YILDIZ F., Javanshir N.

TOPOLOGY AND ITS APPLICATIONS, vol.309, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 309
  • Publication Date: 2022
  • Doi Number: 10.1016/j.topol.2021.107915
  • Journal Name: TOPOLOGY AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Keywords: Metric, Complementary graph, Ramsey's theorem, Antisymmetric T-0-quasi-metric, Symmetric path, Ultra-quasi-pseudometric, Symmetry component, Antisymmetric point, Weighted quasi-metric, Antisymmetrically connected
  • Hacettepe University Affiliated: Yes

Abstract

The concept of antisymmetric T-0-quasi-metric space which is in some sense opposite to metric space appeared rather naturally, within the framework of asymmetry of the T-0-quasi-metric spaces.& nbsp;In this context, some further asymmetric properties and the topological aspects of antisymmetric T-0-quasi-metric spaces are investigated by presenting many crucial results. More specifically, we address the following question: when does a topological space admit an antisymmetric T-0-quasi-metric inducing its topology? Hence, some positive answers to this question are obtained under a few conditions on topological spaces.& nbsp;Besides these, the idea of approximation to T-0-quasi-metrics via antisymmetric T-0-quasi-metrics is discussed for the T-0-quasi-metrics satisfying some additional conditions, as well. (C)& nbsp;2021 Elsevier B.V. All rights reserved.