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...

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Detalles Bibliográficos
Autores: Constantini, Camillo, Kubís, Wieslaw
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:10251/82378
Acceso en línea:https://riunet.upv.es/handle/10251/82378
Access Level:acceso abierto
Palabra clave:Hyperspace
Wijsman topology
Hausdorff metric
Path-wise connectedness
Absolute retract
Descripción
Sumario:[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.