Countable covers and uniform closure
We present, in a unified way, several results of uniform approximation for real-valued continuous and uniformly continuous functions on a space X . We obtain all of them by applying a general method of proof that involves a certain kind of countable covers of X , the so-called 2-finite covers. For i...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 1999 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/58532 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/58532 |
| Access Level: | acceso abierto |
| Palavra-chave: | 515.1 uniform approximation uniform closure and 2-unite cover Topología 1210 Topología |
| Resumo: | We present, in a unified way, several results of uniform approximation for real-valued continuous and uniformly continuous functions on a space X . We obtain all of them by applying a general method of proof that involves a certain kind of countable covers of X , the so-called 2-finite covers. For instance, if X is endowed with the weak uniformity given by a vector lattice F of real-valued functions on X containing all the real constant functions then, using that method, we characterize the uniform density of F only in terms of the family F , thus improving a previous result in this line. |
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