Probabilistic uniformities of uniform spaces
[EN] Usually, fuzzy metric spaces are endowed with crisp topologies or crisp uniformities. Nevertheless, some authors have shown how to construct in this context different kinds of fuzzy uniformities like a Hutton [0, 1]- quasi-uniformity or a probabilistic uniformity. In 2010, J. Guti´errez Garc´ıa...
| Autores: | , , |
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| Tipo de recurso: | capítulo de libro |
| 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:10251/128037 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/128037 |
| Access Level: | acceso abierto |
| Palabra clave: | Fuzzy metric space Fuzzy gauge base Probabilistic uniformity |
| Sumario: | [EN] Usually, fuzzy metric spaces are endowed with crisp topologies or crisp uniformities. Nevertheless, some authors have shown how to construct in this context different kinds of fuzzy uniformities like a Hutton [0, 1]- quasi-uniformity or a probabilistic uniformity. In 2010, J. Guti´errez Garc´ıa, S. Romaguera and M. Sanchis [7] proved that the category of uniform spaces is isomorphic to a category whose objects are sets endowed with a fuzzy uniform structure, i. e. a family of fuzzy pseudometrics satisfying certain conditions. We will show here that, by means of this isomorphism, we can obtain several methods to endow a uniform space with a probabilistic uniformity. Furthermore, we obtain a factorization of some functors introduced in [6]. |
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