Hybrid topologies on the real line
[EN] 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 lowerlimit topolog...
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| Format: | Article |
| Publication date: | 2023 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/193024 |
| Online Access: | https://riunet.upv.es/handle/10251/193024 |
| Access Level: | Open access |
| Keyword: | Hybrid topology Hattori topology Quasi-metric |
| Summary: | [EN] 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 lowerlimit 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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