Comparison of Hyperspace and Function Space Topologies
by
R.A. McCoy
Virginia Tech

By imposing appropriate topologies, the set 2^X×Y, of all closed subsets of X×Y, can be considered as both a hyperspace and a function space. We look at two hyperspace topologies and two function space topologies on 2^X×Y and compare them. For each pair of these four topologies, we give necessary and sufficient conditions on X and Y in order that the first topology is finer than the second. Also we consider what kind of subspace C(X, Y) is, where C(X, Y) is the set of continuous functions from X to Y.

Date received: January 27, 1998