On the topological locality of antisymmetric connectedness

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.