Metrizabilidade de topologias e distâncias generalizadas
In this work, we present a study on the metrizability of topologies presenting the necessary conditions for a topology to be metrizable, i.e., it can be constructed starting from a metric originating from open balls. In addition, several interesting examples of topologies are presented to show that...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | Brasil |
| Institución: | Universidade Federal do Rio Grande do Norte (UFRN) |
| Repositorio: | Repositório Institucional da UFRN |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufrn.br:123456789/28928 |
| Acceso en línea: | https://repositorio.ufrn.br/jspui/handle/123456789/28928 |
| Access Level: | acceso abierto |
| Palabra clave: | Topologia metrizável i-Métrica V-Valorada Topologia i-Quasi-Pseudome-trizável Métrica intervalar CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| Sumario: | In this work, we present a study on the metrizability of topologies presenting the necessary conditions for a topology to be metrizable, i.e., it can be constructed starting from a metric originating from open balls. In addition, several interesting examples of topologies are presented to show that many of the presented are only necessary. Moreover, the Nagata-Smirnov Bing theorem is also mentioned, which presents necessary and sufficient conditions for a topology to be metrizable. In addition, we present a generalization of the concept of metric, which is called V-valued i-metric. Through this generalization we define the concepts of V-valued i-quasi-metric, V-valued i-pseudometric and V-valued iquasipseudometric and it is proved that every topology is i-quasi-pseudometrizable. Based on the theory of interval math an interval metric is constructed which is a particular case of i-metric. This interval metric also generates a topology and we assess whether this topology is metrizable. |
|---|