Di-uniform texture spaces
[EN] Textures were introduced by the second author as a point-based setting for the study of fuzzy sets, and have since proved to be an appropriate framework for the development of complement-free mathematical concepts. In this paper the authors lay the foundation for a theory of uniformities in a t...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2003 |
| 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:10251/82344 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/82344 |
| Access Level: | acceso abierto |
| Palabra clave: | Uniformity Texturing Direlation Difunction Di-uniform texture space Uniform ditopology Uniform bicontinuity Initial di-uniformity Separation Dimetric Complement-free Point-free Fuzzy set |
| Sumario: | [EN] Textures were introduced by the second author as a point-based setting for the study of fuzzy sets, and have since proved to be an appropriate framework for the development of complement-free mathematical concepts. In this paper the authors lay the foundation for a theory of uniformities in a textural context. Analogues are given for both the diagonal and covering approaches to the classical theory of uniform structures, the notion of uniform topology is generalized and an analogue given for the well known result that a topological space is uniformizable if and only if it is completely regular. Finally a textural analogue of the classical interplay between uniformities and families of pseudo-metrics is presented. |
|---|