Symmetrically connected and antisymmetrically connected T0-quasi-metric extensions
Topology and its Applications, cilt.276, 2020 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 276
- Basım Tarihi: 2020
- Doi Numarası: 10.1016/j.topol.2020.107179
- Dergi Adı: Topology and its Applications
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Anahtar Kelimeler: Antisymmetric path, Antisymmetric point, Antisymmetrically connected extension, Connected complementary graph, Isometry, Remainder, Symmetric pair, Symmetrically connected space, Symmetry graph, T0-quasi-metric
- Ankara Yıldırım Beyazıt Üniversitesi Adresli: Hayır
Özet
In this paper, the authors introduce and study the notions of symmetrically connected extension and antisymmetrically connected extension for T0-quasi-metric spaces which satisfy some special conditions, with the help of two types of connectedness, described in the sense of asymmetric topology. In particular, the facts that each bounded T0-quasi-metric space has a symmetrically connected one-point extension and each metric space has an antisymmetrically connected one-point extension are proved. Also, several observations on some specific examples of symmetrically connected T0-quasi-metric extensions are presented in relation to the connectedness of the graphs, in the sense of graph theory. Furthermore, in order to give some answers for the natural question whether each T0-quasi-metric space has a one-point antisymmetrically connected extension or not, we prove some stronger results for the antisymmetrically connected extensions, by describing a weaker notion which is a generalization of boundedness.