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Infima of hyperspace topologies

Part of: Basic constructions

Published online by Cambridge University Press:  26 February 2010

C. Costantini ,
S. Levi  and
J. Pelant
C. Costantini
Affiliation:
Dipartimento di Matematica, Universitá di Milano, Via Saldini 50, 20133 Milano, Italy.
S. Levi
Affiliation:
Dipartimento di Matematica, Universitá di Milano, 20133 Milano, Italy.
J. Pelant
Affiliation:
Czech Academy of Sciences, Department of Mathematics, Žitná 25, 11567 Praha 1, Czech Republic.
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Abstract

We study infima of families of topologies on the hyperspace of a metrizable space. We prove that Kuratowski convergence is the infimum, in the lattice of convergences, of all Wijsman topologies and that the cocompact topology on a metric space which is complete for a metric d is the infimum of the upper Wijsman topologies arising from metrics that are uniformly equivalent to d.

MSC classification

Secondary: 54B20: Hyperspaces
Type
Research Article
Information
Mathematika , Volume 42 , Issue 1 , June 1995 , pp. 67 - 86
Copyright
Copyright © University College London 1995

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