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Antiproximinal Sets in Banach Spaces of Continuous Vector-Valued Functions

✍ Scribed by Ştefan Cobzaş

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
123 KB
Volume
261
Category
Article
ISSN
0022-247X

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✦ Synopsis

A closed nonvoid subset Z of a Banach space X is called antiproximinal if no point outside Z has a nearest point in Z. The aim of the present paper is to prove that, for a compact Hausdorff space T and a real Banach space E, the Banach space C T E , of all continuous functions defined on T and with values in E, contains an antiproximinal bounded closed convex body. This extends a result proved by V.

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