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On Covering the Unit Ball in Normed Spaces

Published online by Cambridge University Press:  20 November 2018

J. Connett
J. Connett*
Affiliation:
Northern Illinois University, DeKalb, Illinois
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By compactness, the unit ball Bn in Rn has a finite covering by translates of rBn, for any r > 0. The main theorem of this note shows that a weaker covering property does not hold in any infinite-dimensional normed space.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 107 - 109
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Kantorovich, L. V. and Akilov, G. P., Functional analysis in normed spaces, Macmillan, New York, 1964.Google Scholar