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A generalized Banach-Mazur theorem

Published online by Cambridge University Press:  17 April 2009

Martin Kleiber  and
W. J. Pervin
Martin Kleiber
Affiliation:
Villanova University, Villanova, Pa. (USA).
W. J. Pervin
Affiliation:
Drexel Institute of Technology Philadelphia, Pa. 19104 (USA).
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Abstract

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For every infinite cardinal a we let Ca, be the set of all real-valued continuous functions on a product of a closed unit intervals with the supmetric. It is shown that Ca has separability degree a. Further, the classical theorem of Banach and Mazur is generalized by showing that every metric space of separability degree a is isometric to a subspace of ca

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 2 , August 1969 , pp. 169 - 173
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Banach, Stefan, Théorie des opérations linéaires, (Monografie Matematyczne, Warszawa, 1932).Google Scholar
[2]Sierpinski, W., General Topology, (University of Toronto Press, Toronto, 1952).CrossRefGoogle Scholar