The locally finite topology on

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

Journal:
Proc. Amer. Math. Soc. **101** (1987), 168-172

MSC:
Primary 54B20; Secondary 54A10

DOI:
https://doi.org/10.1090/S0002-9939-1987-0897090-2

MathSciNet review:
897090

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Abstract | References | Similar Articles | Additional Information

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

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0897090-2

Keywords:
Hyperspaces,
locally finite topology,
Vietoris topology,
Hausdorff metric topology,
supremum topology,
coincidences,
UC space

Article copyright:
© Copyright 1987
American Mathematical Society