Given a metric space (X, d) the hyperspace 2X consisting of all nonempty closed subsets is equipped with the Wijsman Topology Tw(d). If on 2^X one considers the source of all distance functions d(.,S), for S running through all nonempty closed subsets of X then the Wijsman topology is the initial lift in Top of this source. In this paper the existence of isolated points in the hyperspace is studied. Moreover it is shown that every Tychonoff space can be embedded as a closed subspace in the Wijsman hyperspace of a complete metric space which is locally R.
|Publication status||Published - 2012|
Bibliographical noteAmerican Mathematical Society
- Wijsman hyperspace