Research Information System
Topology and its Applications, 2025 (SCI-Expanded)
The locality status of an antisymmetrically connected T0-quasi-metric space was described in our previous studies, under the name local antisymmetric connectedness. Thus we examined the cases under which conditions a T0-quasi-metric space would become locally antisymmetrically connected. Moreover, various topological characterizations of locally antisymmetrically connected T0-quasi-metric spaces were presented via metrics. Specifically, as a natural approach in the context of asymmetric topology, some different aspects of the theory of local antisymmetric connectedness were discussed for the T0-quasi-metrics generated by asymmetric norms. In this paper, many further observations about the local antisymmetric connectedness are dealt with especially in the sense of their products, unions and heritability with respect to subspaces or superspaces via theorems and (counter)examples in the context of T0-quasi-metrics. Besides these, it is natural to ask whether the images of locally antisymmetrically connected spaces under an isometry have the same property or not, and this question will be also discussed here as another problem worth examining.