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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Nonexistence of continuous selections of the metric projection for a class of weak Chebyshev spaces
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by Manfred Sommer PDF
Trans. Amer. Math. Soc. 260 (1980), 403-409 Request permission

Abstract:

The class $\mathfrak {B}$ of all those n-dimensional weak Chebyshev subspaces of $C [a, b]$ whose elements have no zero intervals is considered. It is shown that there does not exist any continuous selection of the metric projection for G if there is a nonzero g in G having at least $n + 1$ distinct zeros. Together with a recent result of Nürnberger-Sommer, the following characterization of continuous selections for $\mathfrak {B}$ is valid: There exists a continuous selection of the metric projection for G in $\mathfrak {B}$ if and only if each nonzero g in G has at most n distinct zeros.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 260 (1980), 403-409
  • MSC: Primary 41A65; Secondary 41A50, 41A52
  • DOI: https://doi.org/10.1090/S0002-9947-1980-0574787-3
  • MathSciNet review: 574787