Existence of chebyshev centers, best //-nets and best compact approximants

Dan Amir, Jaroslav Mach, Klaus Saatkamp

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we investigate the existence and continuity of Chebyshev centers, best «-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 C M is constructed which has no Chebyshev center, no best n-net and not best compact set approximant.

Original languageEnglish
Pages (from-to)513-524
Number of pages12
JournalTransactions of the American Mathematical Society
Volume271
Issue number2
DOIs
StatePublished - Jun 1982

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