On weak Chebyshev subspaces. II. Continuous selection for the metric projection and extension to Mairhuber's theorem

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Abstract

The main result in this paper is the characterization of all n-dimensional weak Chebyshev Z subspaces of C(Q) for which the metric projection has a continuous selection. It is also shown that if n ≥ 3 and PN has a continuous selection, then Q should be homeomorphic to a subset of R.

Original languageEnglish
Pages (from-to)142-163
Number of pages22
JournalJournal of Approximation Theory
Volume67
Issue number2
DOIs
Publication statusPublished - 1991

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Continuous Selection
Metric Projection
Chebyshev
Subspace
Homeomorphic
Theorem
n-dimensional
Subset

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Mathematics(all)
  • Applied Mathematics

Cite this

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abstract = "The main result in this paper is the characterization of all n-dimensional weak Chebyshev Z subspaces of C(Q) for which the metric projection has a continuous selection. It is also shown that if n ≥ 3 and PN has a continuous selection, then Q should be homeomorphic to a subset of R.",
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