Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces


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Javanshir N., YILDIZ F.

Universal Journal of Mathematics and Applications, vol.6, no.3, pp.100-105, 2023 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.32323/ujma.1323655
  • Journal Name: Universal Journal of Mathematics and Applications
  • Journal Indexes: Scopus
  • Page Numbers: pp.100-105
  • Keywords: Antisymmetric path, Antisymmetry component, Asymmetrically normed real vector space, Complementary graph, Connected graph, Local antisymmetric connectedness, Symmetric pair, Symmetrization metric, T0-quasi-metric
  • Hacettepe University Affiliated: Yes

Abstract

In this paper, some properties of locally antisymmetrically connected spaces which are the localized version of the antisymmetrically connected T0-quasi-metric spaces constructed as the natural counterparts of connected complementary graphs, are presented in terms of asymmetric norms. According to that, we investigated some different aspects and examples of local antisym-metric connectedness in the framework of asymmetrically normed real vector spaces. Specifically, it is proved that the structures of antisymmetric connectedness and local antisymmetric connectedness coincide for the T0-quasi-metrics induced by the asymmetric norms which associate the theory of quasi-metrics with functional analysis.