Set-Valued Analysis

, Volume 2, Issue 1–2, pp 135–139 | Cite as

A splitting property of the upper bounded-Hausdorff convergence

  • C. Costantini
Article
  • 22 Downloads

Abstract

We provide a characterization, based on a splitting property, for the upper bounded-Hausdorff convergence of a net of closed sets. Furthermore, we use this property to describe the local structure of the upper bounded-Hausdorff topology.

Mathematics Subject Classifications (1991)

Primary: 54B20 Secondary: 54A20 54D05 

Key words

Hyperspace of a metric space upper Hausdorff and upper bounded-Hausdorff convergence splitting property 

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References

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    Attouch, H., Lucchetti, R., and Wets, R. J.-B.: The topology of the ρ-Hausdorff distance,Ann. Mat. Pura Appl. (4 160 (1991), 303–320.Google Scholar
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    Beer, G. and Di Concilio, A.: Uniform continuity on bounded sets and the Attouch-Wets topology,Proc. Amer. Math. Soc. 112 (1991), 235–243.Google Scholar
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    Beer, G. and Lucchetti, R.: Well-posed optimization problems and a new topology for the closed subsets of a metric space,Rocky Mountain J. Math., to appear.Google Scholar
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    Penot, J.-P.: The cosmic Hausdorff topology, the bounded Hausdorff topology and continuity of polarity,Proc. Amer. Math. Soc. 113 (1991), 275–285.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • C. Costantini
    • 1
  1. 1.Dipartimento di MatematicaUniversità di MilanoMilanoItaly

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