Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces

Year 2023, , 100 - 105, 30.09.2023

Nezakat Javanshır , Filiz Yıldız

https://doi.org/10.32323/ujma.1323655

Abstract

In this paper, some properties of locally antisymmetrically connected spaces which are the localized version of the antisymmetrically connected $T_0$-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 antisymmetric 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 $T_0$-quasi-metrics induced by the asymmetric norms which
associate the theory of quasi-metrics with functional analysis.

Keywords

Antisymmetry component, Asymmetrically normed real vector space, Antisymmetric path, Complementary graph, Connected graph, Local antisymmetric connectedness, Symmetrization metric, Symmetric pair, $T_0$-quasi-metric

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