Propriedades topológicas de hiperespaços
Given a topological space, one can take the collection of subsets satisfying one or more properties and equip this collection with a topology. As such, this collection is called a hyperspace. In this dissertation, we aim to discuss a wide range of topological properties that hyperspaces can satisfy...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | Brasil |
| Institución: | Universidade Federal de Minas Gerais (UFMG) |
| Repositorio: | Repositório Institucional da UFMG |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufmg.br:1843/58299 |
| Acceso en línea: | http://hdl.handle.net/1843/58299 |
| Access Level: | acceso abierto |
| Palabra clave: | Hiperespaços Hipertopologias Topologia de Vietoris Topologia Uniforme Métrica de Hausdorff Espaços Uniformes Matemática – Teses Hiperespaço - Teses Topologia – Teses Espaços uniformes – Teses |
| Sumario: | Given a topological space, one can take the collection of subsets satisfying one or more properties and equip this collection with a topology. As such, this collection is called a hyperspace. In this dissertation, we aim to discuss a wide range of topological properties that hyperspaces can satisfy depending on the properties the base space satisfies and vice versa. This is done for the Vietoris topology as well as for the uniform topology, which we show coincide with the Hausdorff metric when the space is metric. In order to be able to do it, we review concepts of General Topology and discuss the theory of uniform spaces. |
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