Localization of antisymmetric spaces in the framework of quasi-metrics - Yildiz, Filiz (Topology Proceedings, 2025)
Antisymmetric $T_0$-quasi-metric spaces which are in some sense opposite to metric spaces had appeared in the previous studies rather naturally, within the framework of asymmetry of the $T_0$-quasi-metric spaces. In this paper, the locality status of antisymmetric $T_0$-quasimetrics is described and studied under the name local antisymmetricness. Following that we examine the cases under which conditions a non-metric $T_0$-quasi-metric space would become locally antisymmetric as well as all finite $T_0$-quasi-metric spaces are locally antisymmetric. Moreover, some asymmetric properties of locally antisymmetric $T_0$-quasi-metric spaces are determined via topological perspectives and metrics. As another approach in the context of asymmetric topology, some different aspects of the local antisymmetricness are discussed especially for the $T_0$-quasi-metrics generated by the asymmetric norms.