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A note on compact sets in spaces of subsets

Published online by Cambridge University Press:  17 April 2009

Phil Diamond  and
Peter Kloeden
Phil Diamond
Affiliation:
Mathematics Department, University of Queensland, St. Lucia, Qld 4067, Australia.
Peter Kloeden
Affiliation:
School of Mathematical and Physical Sciences, Murdoch University, Murdoch, W.A. 6150, Australia.
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Abstract

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A simple characterisation is given of compact sets of the space K(X), of nonempty compact subsets of a complete metric space X, with the Hausdorff metric dH. It is used to give a new proof of the Blaschke selection theorem for compact starshaped sets.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 3 , December 1988 , pp. 393 - 395
Copyright
Copyright © Australian Mathematical Society 1988

References

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[3]Hausdorff, F., Set Theory (Chelsea Press, New York, 1957).Google Scholar
[4]Matheron, G., Random Sets and Integral Geometry (John Wiley, New York, 1975).Google Scholar
[5]Weil, W., ‘An application of the central limit theorem for Banach-space-valued random variables to the theory of random sets’, Z. Wahrsch. Verw. Gebiete 60 (1982), 203–208.CrossRefGoogle Scholar