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...
| Autores: | , |
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| 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 |
| 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. |
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