Fuzzy uniform structures
[EN] The concept of fuzzy uniform structure was introduced in [7] as a fuzzy counterpart of the concept of gauge associated with a uniformity. In fact, the category of fuzzy uniform structures is isomorphic to that of uniform spaces. Here, we introduce two other concepts of fuzzy uniform structures...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/102314 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/102314 |
| Access Level: | acceso abierto |
| Palabra clave: | Fuzzy uniform structure Probabilistic uniformity Lowen uniformity Fuzzy metric MATEMATICA APLICADA |
| Sumario: | [EN] The concept of fuzzy uniform structure was introduced in [7] as a fuzzy counterpart of the concept of gauge associated with a uniformity. In fact, the category of fuzzy uniform structures is isomorphic to that of uniform spaces. Here, we introduce two other concepts of fuzzy uniform structures which allow to establish two categories isomorphic to the categories of probabilistic uniform spaces and Lowen uniform spaces, respectively. This sheds light on the relationship between these fuzzy uniformities and classical uniformities. Furthermore, we obtain a factorization of Lowen's adjoint functors omega(*) and iota which establish a relationship between the categories of uniform spaces and Lowen uniform spaces. |
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