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.

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