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Completeness of normed linear spaces admitting centers
Published online by Cambridge University Press: 09 April 2009
Abstract
It is shown that a normed linear space admitting (Chebyshev) centers is complete. Then the ideas in the proof of this fact are used to show that every incomplete CLUR (compactly locally uniformly rotund) normed linear space contains a closed bounded convex subset B with the following properties: (a) B does not contain any farthest point; (b) B does not contain any nearest point (to the elements of its complement).
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 39 , Issue 3 , December 1985 , pp. 360 - 366
- Copyright
- Copyright © Australian Mathematical Society 1985
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