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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Existence of Chebyshev centers, best $ n$-nets and best compact approximants


Authors: Dan Amir, Jaroslav Mach and Klaus Saatkamp
Journal: Trans. Amer. Math. Soc. 271 (1982), 513-524
MSC: Primary 46B20; Secondary 41A46
DOI: https://doi.org/10.1090/S0002-9947-1982-0654848-2
MathSciNet review: 654848
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Abstract: In this paper we investigate the existence and continuity of Chebyshev centers, best $ n$-nets and best compact sets. Some of our positive results were obtained using the concept of quasi-uniform convexity. Furthermore, several examples of nonexistence are given, e.g., a sublattice $ M$ of $ C[0,\,1]$, and a bounded subset $ B \subset M$ is constructed which has no Chebyshev center, no best $ n$-net and not best compact set approximant.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0654848-2
Article copyright: © Copyright 1982 American Mathematical Society