The locally finite topology on 2X

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

doi:10.1090/S0002-9939-1987-0897090-2

The locally finite topology on 2^X

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

Mathematics

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

Let X be a metrizable space. A Vietoris-type topology, called the locally finite topology, is defined on the hyperspace 2^Xof 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 2^Xand when the locally finite topology is metrizable.

Original language	English (US)
Pages (from-to)	168-172
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	101
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1987-0897090-2
State	Published - Sep 1987

Keywords

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

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10.1090/S0002-9939-1987-0897090-2

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