Araştırma Makalesi
Yıl 2024,
Cilt: 53 Sayı: 6, 1647 - 1658, 28.12.2024
Öz
Given a non-empty set $A \subseteq \mathbb{R}$, we consider the smallest topology on $\mathbb{R}$ which contains the open left rays containing points $a \in A$ and the open right rays containing points $b \in \mathbb{R} - A$. We present a natural model for this hybrid topology and show that it is quasi-metrizable. We investigate other variations of this topology.
Anahtar Kelimeler
Destekleyen Kurum
Brno University of Technology
Proje Numarası
MeMoV II no. CZ.02.2.69/0.0/0.0/18-053/0016962.
Teşekkür
The second author acknowledges support from the Brno University of Technology (BUT) under the project MeMoV II no. CZ.02.2.69/0.0/0.0/18-053/0016962.
Kaynakça
- [1] A. Bouziad and E. Sukhacheva, On Hattori spaces, Comment. Math. Univ. Carolin. 58 (2), 213–223, 2017.
- [2] A. Calderón-Villalobos and I. Sánches, Hattori topologies on almost topological groups, Topology Appl. 326, 108411, 15pp., 2023.
- [3] V. A. Chatyrko and Y. Hattori, A poset of topologies on the set of real numbers, Comment. Math. Univ. Carolin. 54 (2), 189–196, 2013.
- [4] V. Chatyrko and A. Karassev, Countable dense homogeneity and Hattori Spaces, Q&A in Gen. Top. 39, 73–87, 2021.
- [5] P. Fletcher and W. F. Lindgren, Quasi-uniformities with a transitive base, Pacific J. Math. 43 (3), 619–631, 1972.
- [6] R. Fox, A short proof of the Junnila quasi-metrization theorem, Proc. AMS 83 (3), 663–664, 1981.
- [7] Y. Hattori, Order and topological structures of posets of the formal balls on metric spaces, Mem. Fac. Sci. Eng. Shimane Univ. Series B: Mathematical Science 43, 13–26, 2010.
- [8] H. H. Hung, Quasi-metrizability, Topology and its Applications 83, 39–43, 1998.
- [9] T. Khmyleva and E. Sukhacheva, On linear hoemomorphisms of spaces of continuous functions on Hattori spaces, Topology Appl. 281, 107209, 8pp., 2020.
- [10] R. D. Kopperman, Which topologies are quasimetrizable?, Topology and its Applications 52, 99–107, 1993.
- [11] H.-P. A. Künzi and F. Yildiz, Extensions of $T_0$-quasi-metrics, Acta Math. Hungar. 153 (1), 196–215, 2017.
- [12] T. Richmond, Hybrid topologies on the real line, Applied General Topology 24 (1) 157–168, 2023.
- [13] T. Richmond, General Topology: An Introduction, De Gruyter, 2020.
- [14] L. A. Steen and J. A. Seeback, Jr., Counterexamples in Topology, (2nd edition) Springer-Verlag, 1970.
Yıl 2024,
Cilt: 53 Sayı: 6, 1647 - 1658, 28.12.2024
Öz
Proje Numarası
MeMoV II no. CZ.02.2.69/0.0/0.0/18-053/0016962.
Kaynakça
- [1] A. Bouziad and E. Sukhacheva, On Hattori spaces, Comment. Math. Univ. Carolin. 58 (2), 213–223, 2017.
- [2] A. Calderón-Villalobos and I. Sánches, Hattori topologies on almost topological groups, Topology Appl. 326, 108411, 15pp., 2023.
- [3] V. A. Chatyrko and Y. Hattori, A poset of topologies on the set of real numbers, Comment. Math. Univ. Carolin. 54 (2), 189–196, 2013.
- [4] V. Chatyrko and A. Karassev, Countable dense homogeneity and Hattori Spaces, Q&A in Gen. Top. 39, 73–87, 2021.
- [5] P. Fletcher and W. F. Lindgren, Quasi-uniformities with a transitive base, Pacific J. Math. 43 (3), 619–631, 1972.
- [6] R. Fox, A short proof of the Junnila quasi-metrization theorem, Proc. AMS 83 (3), 663–664, 1981.
- [7] Y. Hattori, Order and topological structures of posets of the formal balls on metric spaces, Mem. Fac. Sci. Eng. Shimane Univ. Series B: Mathematical Science 43, 13–26, 2010.
- [8] H. H. Hung, Quasi-metrizability, Topology and its Applications 83, 39–43, 1998.
- [9] T. Khmyleva and E. Sukhacheva, On linear hoemomorphisms of spaces of continuous functions on Hattori spaces, Topology Appl. 281, 107209, 8pp., 2020.
- [10] R. D. Kopperman, Which topologies are quasimetrizable?, Topology and its Applications 52, 99–107, 1993.
- [11] H.-P. A. Künzi and F. Yildiz, Extensions of $T_0$-quasi-metrics, Acta Math. Hungar. 153 (1), 196–215, 2017.
- [12] T. Richmond, Hybrid topologies on the real line, Applied General Topology 24 (1) 157–168, 2023.
- [13] T. Richmond, General Topology: An Introduction, De Gruyter, 2020.
- [14] L. A. Steen and J. A. Seeback, Jr., Counterexamples in Topology, (2nd edition) Springer-Verlag, 1970.
Toplam 14 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Proje Numarası | MeMoV II no. CZ.02.2.69/0.0/0.0/18-053/0016962. |
| Erken Görünüm Tarihi | 14 Nisan 2024 |
| Yayımlanma Tarihi | 28 Aralık 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 53 Sayı: 6 |