Paths in hyperspaces

Camillo Constantini, Wieslaw Kubís


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.


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

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1. Hausdorff hyperspaces of R m and their dense subspaces
Wiesław KUBIŚ, Katsuro SAKAI
Journal of the Mathematical Society of Japan  vol: 60  issue: 1  year: 2008  
doi: 10.2969/jmsj/06010193

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147