A Polish Topology for the Closed Subsets of a Polish Space

Gerald Beer
1991 Proceedings of the American Mathematical Society  
Let (X, d) be a complete and separable metric space. The Wijsman topology on the nonempty closed subset CL(A") of X is the weakest topology on CL{X) such that for each x in X , the distance functional A -* d{x, A) is continuous on CL{X). We show that this topology is Polish, and that the traditional extension of the topology to include the empty set among the closed sets is also Polish. We also compare the Borel class of a closed valued multifunction with its Borel class when viewed as a
more » ... viewed as a single-valued function into Ch{X), equipped with Wijsman topology.
doi:10.2307/2048792 fatcat:tjjhtiytrres3hzwu4kcci3zma