Paths in hyperspaces

• Constantini, Camillo ^[2] ; Kubís, Wieslaw ^[1]
  1. [1] University of Silesia

     University of Silesia

     Katowice, Polonia

     
  2. [2] University of Torino
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 4, Nº. 2, 2003, págs. 377-390
• Idioma: inglés
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• Resumen

  • 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.