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...
| Authors: | , , , |
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2019 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87513 |
| Online Access: | https://hdl.handle.net/11441/87513 https://doi.org/10.1016/j.jmaa.2018.11.029 |
| Access Level: | Open access |
| Keyword: | Atsuji space Non-uniformly continuous function Lineability Spaceability Algebrability |
| Summary: | 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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