Structural aspects of the non-uniformly continuous functions and the unbounded functions within C(X)
We prove in this paper that if a metric space supports a real continuous function which is not uniformly continuous then, under appropriate mild assumptions, there exists in fact a plethora of such functions, in both topological and algebraical senses. Corresponding results are also obtained concern...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87513 |
| Acceso en línea: | https://hdl.handle.net/11441/87513 https://doi.org/10.1016/j.jmaa.2018.11.029 |
| Access Level: | acceso abierto |
| Palabra clave: | Atsuji space Non-uniformly continuous function Lineability Spaceability Algebrability |
| Sumario: | We prove in this paper that if a metric space supports a real continuous function which is not uniformly continuous then, under appropriate mild assumptions, there exists in fact a plethora of such functions, in both topological and algebraical senses. Corresponding results are also obtained concerning unbounded continuous functions on a non-compact metrizable space. |
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