Space of quasicontinuous functions with the topology of uniform convergence on semi-compacta

[EN] We introduce a new set-open topology on function spaces namely the semi-compact-open topology. The topology of uniform convergence on semi-compacta lies between the topology of pointwise convergence and the topology of uniform convergence. We show that for the space of quasicontinuous functions...

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Detalles Bibliográficos
Autores: Barman, Neelim Kumar, Hazarika, Debajit
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:dnet:riunet______::592087eb41de4faab94ebf9bde5d1ca8
Acceso en línea:https://riunet.upv.es/handle/10251/234566
Access Level:acceso abierto
Palabra clave:Quasicontinuous functions
Function space
Cardinality properties
Induced functions
Semi-compactness
Descripción
Sumario:[EN] We introduce a new set-open topology on function spaces namely the semi-compact-open topology. The topology of uniform convergence on semi-compacta lies between the topology of pointwise convergence and the topology of uniform convergence. We show that for the space of quasicontinuous functions the topology of uniform convergence on semi-compacta coincides with the semi-compact-open topology. We also investigate results relating to induced functions,  cardinal invariants and Ascoli like properties on the space of quasicontinuous functions when equipped with the topology of uniform convergence on semi-compacta.