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

Amir, Dan; Mach, Jaroslav; Saatkamp, Klaus

doi:10.1090/S0002-9947-1982-0654848-2

Existence of Chebyshev centers, best $n$-nets and best compact approximants
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by Dan Amir, Jaroslav Mach and Klaus Saatkamp PDF

Trans. Amer. Math. Soc. 271 (1982), 513-524 Request permission

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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