Paths in hyperspaces


  • Camillo Constantini University of Torino
  • Wieslaw Kubís University of Silesia



Hyperspace, Wijsman topology, Hausdorff metric, Path-wise connectedness, Absolute retract


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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Author Biographies

Camillo Constantini, University of Torino

Department of Mathematics

Wieslaw Kubís, University of Silesia

Institute of Mathematics


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How to Cite

C. Constantini and W. Kubís, “Paths in hyperspaces”, Appl. Gen. Topol., vol. 4, no. 2, pp. 377–390, Oct. 2003.