Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T03:07:31.507Z Has data issue: false hasContentIssue false

A note on compact sets in spaces of subsets

Published online by Cambridge University Press:  17 April 2009

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Beer, G. A., ‘Starshaped sets and the Hausdorff metric’, Pacific J. Math. 61 (1975), 2127.CrossRefGoogle Scholar
[2]Diamond, P. and Kloeden, P., ‘Characterization of compact subsets of fuzzy sets’, Fuzzy Sets and Systems (1989) (to appear).CrossRefGoogle Scholar
[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), 203208.CrossRefGoogle Scholar