Hybrid topologies on the real line

Tom Richmond

Ayuda

Hybrid topologies on the real line

Richmond, Tom ^[1]
1. [1] Western Kentucky University
  
  Western Kentucky University
  
  Estados Unidos
Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 24, Nº. 1, 2023, págs. 157-168
Idioma: inglés
DOI: 10.4995/agt.2023.18566
Enlaces
- Texto completo
Resumen
- Given A ⊆ ℝ , the Hattori space H(A) is the topological space ( ℝ , τA ) where each a ∈ A has a τA -neighborhood base { ( a − ε , a + ε ) : ε > 0 } and each b ∈ ℝ − A has a τA -neighborhood base { [ b , b + ε ) : ε > 0 } . Thus, τA may be viewed as a hybrid of the Euclidean topology and the lower-limit topology. We investigate properties of Hattori spaces as well as other hybrid topologies on ℝ using various combinations of the discrete, left-ray, lower-limit, upper-limit, and Euclidean topologies. Since each of these topologies is generated by a quasi-metric on ℝ, we investigate hybrid quasi-metrics which generate these hybrid topologies.
Referencias bibliográficas
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- V. A. Chatyrko and Y. Hattori, A poset of topologies on the set of real numbers, Comment. Math. Univ. Carolin. 54, no. 2 (2013), 189-196.
- Y. Hattori, Order and topological structures of posets of the formal balls on metric spaces, Mem. Fac. Sci. Eng. Shimane Univ. Series B: Mathematical...
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- T. Richmond, General Topology: An Introduction, De Gruyter, Berlin, 2020. https://doi.org/10.1515/9783110686579