On equidistant sets in normed linear spaces
- 1 December 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 11 (3) , 443-454
- https://doi.org/10.1017/s0004972700044075
Abstract
In this note some results concerning the equidistant setE(−x, x) and the kernelMθof the metric projectionPM, whereMis a Chebyshev subspace of a normed linear spaceX, have been obtained. In particular, whenX=lp(1 <p< ∞), it has been proved that every equidistant set is closed in thebw-topology of the space. Inc0no equidistant set has this property.Keywords
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- ON THE CONTINUITY OF BEST APPROXIMATION OPERATORSPublished by Walter de Gruyter GmbH ,1972