The locally finite topology on 2X

G. A. Beer, C. J. Himmelberg, K. Prikry, F. S. Van Vleck

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


Let X be a metrizable space. A Vietoris-type topology, called the locally finite topology, is defined on the hyperspace 2Xof all closed, nonempty subsets of X. We show that the locally finite topology coincides with the supremum of all Hausdorff metric topologies corresponding to equivalent metrics on X. We also investigate when the locally finite topology coincides with the more usual topologies on 2Xand when the locally finite topology is metrizable.

Original languageEnglish (US)
Pages (from-to)168-172
Number of pages5
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - Sep 1987


  • Coincidences
  • Hausdorff metric topology
  • Hyperspaces
  • Locally finite topology
  • Supremum topology
  • UC space
  • Vietoris topology


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