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...

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Detalles Bibliográficos
Autor: Richmond, Tom
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/193024
Acceso en línea:https://riunet.upv.es/handle/10251/193024
Access Level:acceso abierto
Palabra clave:Hybrid topology
Hattori topology
Quasi-metric
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repository_id_str
spelling Hybrid topologies on the real lineRichmond, TomHybrid topologyHattori topologyQuasi-metric[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.Universitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20232023-04-05journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/193024reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1930242026-06-13T07:49:27Z
dc.title.none.fl_str_mv Hybrid topologies on the real line
title Hybrid topologies on the real line
spellingShingle Hybrid topologies on the real line
Richmond, Tom
Hybrid topology
Hattori topology
Quasi-metric
title_short Hybrid topologies on the real line
title_full Hybrid topologies on the real line
title_fullStr Hybrid topologies on the real line
title_full_unstemmed Hybrid topologies on the real line
title_sort Hybrid topologies on the real line
dc.creator.none.fl_str_mv Richmond, Tom
author Richmond, Tom
author_facet Richmond, Tom
author_role author
dc.contributor.none.fl_str_mv Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Hybrid topology
Hattori topology
Quasi-metric
topic Hybrid topology
Hattori topology
Quasi-metric
description [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.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-04-05
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/193024
url https://riunet.upv.es/handle/10251/193024
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de València
publisher.none.fl_str_mv Universitat Politècnica de València
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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