Function Spaces and Strong Variants of Continuity
[EN] It is shown that if domain is a sum connected space and range is a T0-space, then the notions of strong continuity, perfect continuity and cl-supercontinuity coincide. Further, it is proved that if X is a sum connected space and Y is Hausdorff, then the set of all strongly continuous (perfectly...
| Autores: | , |
|---|---|
| Tipo de documento: | artigo |
| Data de publicação: | 2008 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositório: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglês |
| OAI Identifier: | oai:riunet.upv.es:10251/85930 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/85930 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Strongly continuous function Perfectly continuous function cl-supercontinuous function Sum connected spaces k-space Topology of point wise convergence Topology of uniform convergence on compacta Compact open topology Equicontinuity Even continuit |
| Resumo: | [EN] It is shown that if domain is a sum connected space and range is a T0-space, then the notions of strong continuity, perfect continuity and cl-supercontinuity coincide. Further, it is proved that if X is a sum connected space and Y is Hausdorff, then the set of all strongly continuous (perfectly continuous, cl-supercontinuous) functions is closed in Y X in the topology of pointwise convergence. The results obtained in the process strengthen and extend certain results of Levine and Naimpally. |
|---|