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Some properties of the Hausdorff distance in metric spaces

Published online by Cambridge University Press:  17 April 2009

Józef Banaś
Affiliation:
Department of Mathematics, Technical University of Rzeszow, 35–959 Rzeszow, W. Pola 2, Poland
Antonio Martinón
Affiliation:
Department of Mathematical Analysis, University of La Laguna, 38271 La Laguna (Tenerife), Spain
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Abstract

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Some properties of the Hausdorff distance in complete metric spaces are discussed. Results obtained in this paper explain ideas used in the theory of measures of noncompactness.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Akmerov, R.R., Kamenskii, M.I., Potapov, A.S., Rodkina, A.E. and Sadovskii, B.N., Measures of noncompactness and condensing operators (Nauka, Novosibinsk, Russian, 1986).Google Scholar
[2]Banaś, J. and Goebel, K., Measures of noncompactness in Banach, spaces: Lecture Notes in Pure and Applied Mathematics 60 (Marcel Dekker, New York, 1980).Google Scholar
[3]Daneš, J., ‘On densifying and related mappings and their applications in nonlinear functional analysis’, in Theory of nonlinear operators, pp. 1556 (Akademie-Verlag, Berlin, 1974).Google Scholar
[4]Duc, D.M., ‘Measure of noncompactness and spectral theory’, Math. Nachr. 115 (1984), 305317.CrossRefGoogle Scholar
[5]Kuratowski, K., Topology (Academic Press, 1966).Google Scholar
[6]Martinon, A., ‘A system of axioms for measures of noncompactness’, Extracta Math. 4 (1989), 4446.Google Scholar
[7]Weis, L.W., ‘On the computation of some quantities related to semi-Fredholm operators’, in Proc. 12th Winter School on Abstract Analysis (Srni, Bohemian Forest, 1984).Google Scholar