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Compactness and local compactness in hyperspaces

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
123
Issue
3
Identifiers
DOI: 10.1016/s0166-8641(01)00222-x
Keywords
  • Hyperspace
  • Vietoris Hypertopology
  • Hausdorff Hypertopology
  • Wijsman Hypertopology
  • Compact Space
  • Relatively Compact Subspace
  • Locally Compact Space
Disciplines
  • Mathematics

Abstract

Abstract We give characterizations for a subspace of a hyperspace, endowed with either the Vietoris or the Wijsman topology, to be compact or relatively compact. Then we characterize—both globally and at the single points—the local compactness of a hyperspace, endowed with either the Vietoris, the Wijsman, or the Hausdorff metric topology. Several examples illustrating the behaviour of local compactness are also included.

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