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On equidistant sets in normed linear spaces

Published online by Cambridge University Press:  17 April 2009

B.B. Panda  and
O.P. Kapoor
B.B. Panda
Affiliation:
Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur, India.
O.P. Kapoor
Affiliation:
Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur, India.
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Abstract

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In this note some results concerning the equidistant set E(−x, x) and the kernel Mθ of the metric projection PM, where M is a Chebyshev subspace of a normed linear space X, have been obtained. In particular, when X = lp (1 < p < ∞), it has been proved that every equidistant set is closed in the bw-topology of the space. In c0 no equidistant set has this property.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 3 , December 1974 , pp. 443 - 454
Copyright
Copyright © Australian Mathematical Society 1974

References

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