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: | ; |
|---|---|
| Tipo de documento: | Artículo |
| Fecha de publicación: | 2003 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Lenguaje: | Inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/82378 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/82378 |
| Nivel de acceso: | Acceso abierto |
| Palabra clave: | Hyperspace Wijsman topology Hausdorff metric Path-wise connectedness Absolute retract |
| _version_ | 1878735996839788544 |
|---|---|
| author | Constantini, Camillo |
| author2 | Kubís, Wieslaw |
| author2_role | author |
| author_browse | Constantini, Camillo Kubís, Wieslaw |
| author_facet | Constantini, Camillo Kubís, Wieslaw |
| author_role | author |
| collection | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| description | [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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_86f09d0e18084a7fcea99f53c54a92fe |
| institution | Universitat Politècnica de València (UPV) |
| instname_str | Universitat Politècnica de València (UPV) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:riunet.upv.es:10251/82378 |
| publishDate | 2003 |
| publishDateSort | 2003 |
| publisher | Universitat Politècnica de València |
| publisherStr | Universitat Politècnica de València |
| reponame_str | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| spelling | Paths in hyperspaces Constantini, Camillo Kubís, Wieslaw Hyperspace Wijsman topology Hausdorff metric Path-wise connectedness Absolute retract [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. The research was supported by KBN Grant No. 5P03A04420 Universitat Politècnica de València https://riunet.upv.es/handle/10251/82378 |
| spellingShingle | Paths in hyperspaces Constantini, Camillo Hyperspace Wijsman topology Hausdorff metric Path-wise connectedness Absolute retract |
| title | Paths in hyperspaces |
| title_full | Paths in hyperspaces |
| title_fullStr | Paths in hyperspaces |
| title_full_unstemmed | Paths in hyperspaces |
| title_short | Paths in hyperspaces |
| title_sort | Paths in hyperspaces |
| topic | Hyperspace Wijsman topology Hausdorff metric Path-wise connectedness Absolute retract |
| topic_facet | Hyperspace Wijsman topology Hausdorff metric Path-wise connectedness Absolute retract |
| url | https://riunet.upv.es/handle/10251/82378 |