Orderability and continuous selections for Wijsman and Vietoris hyperspaces
by
Debora DiCaprio
York University
Coauthors: Stephen Watson (York University)

Let CL(X) denote the set of all nonempty closed subsets of a topological space X. A continuous selection for CL(X) is any map f\colon CL(X) --> X which is continuous with respect to the hypertopology on CL(X) and such that f(C) in C for every C in CL(X). We show that subject to natural conditions, the base space admits a closed order such that the minimum map is a continuous selection for many standard hyperspace topologies including the Vietoris and the Wijsman topology. In particular, we conclude that Polish spaces satisfying these conditions can be endowed with a compatible order and that the minimum function is a continuous selection for the Wijsman topology, just as it is for [0, 1]. This not only completes a result of Bertacchi and Costantini (1998), but also solves a problem implicitely raised in their paper.

Date received: February 25, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajz-56.