Paths in hyperspaces

Camillo Constantini; Wieslaw Kubís

doi:10.4995/agt.2003.2040

Authors

Camillo Constantini University of Torino
Wieslaw Kubís University of Silesia

DOI:

https://doi.org/10.4995/agt.2003.2040

Keywords:

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

Abstract

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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