On the topological locality of antisymmetric connectedness

YILDIZ F., Javanshir N.

Filomat, vol.37, no.12, pp.3883-3890, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 12
  • Publication Date: 2023
  • Doi Number: 10.2298/fil2312883y
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.3883-3890
  • Keywords: &nbsp, Quasi-pseudometric, complementary graph, symmetric pair, antisymmetric path, symmetry graph, T0-quasi-metric space, antisymmetry component, locally antisymmetrically connected space
  • Hacettepe University Affiliated: Yes

Abstract

The theory of antisymmetric connectedness for a T0-quasi-metric space was established in terms of graph theory lately, as corresponding counterpart of the connectedness for the complement of a graph. Following that in the current study, a topological localized version of the antisymmetrically connected spaces is described and studied through a variety of approaches in the context of T0-quasi-metrics. Within the framework of this, we examine the cases under which conditions a T0-quasi-metric space would become locally antisymmetrically connected as well as some topological characterizations of locally antisymmetrically connected T0-quasi-metric spaces are presented, especially via metrics.