Certain observations on antisymmetric T0-quasi-metric spaces
Topology and its Applications, cilt.309, 2022 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 309
- Basım Tarihi: 2022
- Doi Numarası: 10.1016/j.topol.2021.107915
- Dergi Adı: Topology and its Applications
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Anahtar Kelimeler: Antisymmetric point, Antisymmetric T0-quasi-metric, Antisymmetrically connected, Complementary graph, Metric, Ramsey's theorem, Symmetric path, Symmetry component, Ultra-quasi-pseudometric, Weighted quasi-metric
- Ankara Yıldırım Beyazıt Üniversitesi Adresli: Evet
Özet
The concept of antisymmetric T0-quasi-metric space which is in some sense opposite to metric space appeared rather naturally, within the framework of asymmetry of the T0-quasi-metric spaces. In this context, some further asymmetric properties and the topological aspects of antisymmetric T0-quasi-metric spaces are investigated by presenting many crucial results. More specifically, we address the following question: when does a topological space admit an antisymmetric T0-quasi-metric inducing its topology? Hence, some positive answers to this question are obtained under a few conditions on topological spaces. Besides these, the idea of approximation to T0-quasi-metrics via antisymmetric T0-quasi-metrics is discussed for the T0-quasi-metrics satisfying some additional conditions, as well.