SOME REMARKS FOR THE ANTISYMMETRICALLY CONNECTED SPACES

Abstract

In the previous studies, the notion of antisymmetrically connected
T0-quasi-metric space is described as a type of the connectivity in the framework
of asymmetric topology. Actually, the theory of antisymmetric connectedness
was established in terms of graph theory, as the natural counterpart of
the connected complementary graph. In this paper, some significant properties
of antisymmetrically connected T0-quasi-metric spaces are presented.
Accordingly, we studied some dierent aspects of the theory of antisymmetric
connectedness in terms of asymmetric norms which associate the theory of
quasi-metrics with functional analysis. In the light of this approach, antisymmetrically
connected T0-quasi-metric spaces are investigated and characterized
First-time in the theory of asymmetrically normed real vector spaces.
Besides these, many further observations about the antisymmetric connectedness
are dealt with especially in the sense of their combinations such as
products and unions through various theorems and examples in the context
of T0-quasi-metrics. Also, we examined the question of under what kind of
quasi-metric mapping it will be preserved.