Paths in hyperspaces
[EN] We prove that the hyperspace of closed bounded sets with the Hausdor_ topology, over an almost convex metric space, is an absolute retract. Dense subspaces of normed linear spaces are examples of, not necessarily connected, almost convex metric spaces. We give some necessary conditions for the...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2003 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositório: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglês |
| OAI Identifier: | oai:riunet.upv.es:10251/82378 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/82378 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Hyperspace Wijsman topology Hausdorff metric Path-wise connectedness Absolute retract |
| Resumo: | [EN] We prove that the hyperspace of closed bounded sets with the Hausdor_ topology, over an almost convex metric space, is an absolute retract. Dense subspaces of normed linear spaces are examples of, not necessarily connected, almost convex metric spaces. We give some necessary conditions for the path-wise connectedness of the Hausdorff metric topology on closed bounded sets. Finally, we describe properties of a separable metric space, under which its hyperspace with the Wijsman topology is path-wise connected. |
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