Locally symmetrically connected T 0-quasi-metric spaces
Quaestiones Mathematicae, cilt.45, sa.3, ss.369-384, 2022 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 45 Sayı: 3
- Basım Tarihi: 2022
- Doi Numarası: 10.2989/16073606.2021.1882602
- Dergi Adı: Quaestiones Mathematicae
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Sayfa Sayıları: ss.369-384
- Anahtar Kelimeler: antisymmetric pair, antisymmetric path, asymmetrically normed real vector space, locally symmetrically connected space, metric, symmetric point, symmetry component, symmetry graph, T 0-quasi-metric
- Ankara Yıldırım Beyazıt Üniversitesi Adresli: Hayır
Özet
Following the theory of symmetrically connected T 0-quasi-metric spaces constructed lately, in the present investigation the authors introduce and study the localized version of symmetric connectedness under the name local symmetric connectedness, as a new approach to determining the degree of the asymmetry and symmetry of T 0-quasi-metric spaces. In this context, some properties and topological aspects of locally symmetrically connected T 0-quasi-metric spaces are discussed by presenting various observations and many concrete (counter)examples. Specifically, it is shown that symmetric connectedness coincides with the local symmetric connectedness if we deal with the T 0-quasi-metric induced by an asymmetric norm which associates the theory of quasi-metrics in asymmetric topology with functional analysis.