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Mat. Zametki, 1975, Volume 18, Issue 1, Pages 67–76 (Mi mz7627)  

This article is cited in 3 scientific papers (total in 3 papers)

Conditional Chebyshev center of a bounded set of continuous functions

A. L. Garkavi, V. N. Zamyatin


Abstract: Subspaces $\{\mathscr L^n\}$ of codimension $n<\infty$ of the space $C(T)$ of functions, continuous in a bicompactum $T$, are considered. A criterion, whereby a subspace $\mathscr L^n$, contains a Chebyshev center for any bounded set of $C(T)$, is established in terms of the properties of the supports of measures which are annihilated in $\mathscr L^n$. This criterion is equivalent to the following conditions: $\mathscr L^n$ contains an element of best approximation for every $x\in C(T)$, and the support of every measure, which is annihilated in $\mathscr L^n$, is extremally unconnected with respect to the bicompactum $T$.

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English version:
Mathematical Notes, 1975, 18:1, 622–627

Bibliographic databases:

Received: 24.06.1974

Citation: A. L. Garkavi, V. N. Zamyatin, “Conditional Chebyshev center of a bounded set of continuous functions”, Mat. Zametki, 18:1 (1975), 67–76; Math. Notes, 18:1 (1975), 622–627

Citation in format AMSBIB
\Bibitem{GarZam75}
\by A.~L.~Garkavi, V.~N.~Zamyatin
\paper Conditional Chebyshev center of a bounded set of continuous functions
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 1
\pages 67--76
\mathnet{http://mi.mathnet.ru/mz7627}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=385416}
\zmath{https://zbmath.org/?q=an:0321.41026}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 1
\pages 622--627
\crossref{https://doi.org/10.1007/BF01461143}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Vasil'eva, “Closed spans in vector-valued function spaces and their approximative properties”, Izv. Math., 68:4 (2004), 709–747  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. R. Alimov, “Preservation of approximative properties of subsets of Chebyshev sets and suns in $\ell^\infty (n)$”, Izv. Math., 70:5 (2006), 857–866  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. A. R. Alimov, “Monotone path-connectedness of $R$-weakly convex sets in the space $C(Q)$”, J. Math. Sci., 185:3 (2012), 360–366  mathnet  crossref
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