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Mat. Zametki, 1976, Volume 19, Issue 2, Pages 267–278 (Mi mz7746)  

This article is cited in 10 scientific papers (total in 10 papers)

Connectedness and solar properties of sets in normed linear spaces

B. A. Koscheev

Institute of Mathematics and Mechanics, Ural Scientific Center of the AS of USSR

Abstract: The connectedness of certain classes of suns is studied. In particular, it is proved that a compact sun is connected in a normed space. Every gamma sun is connected in a uniformly non-square Banach space.

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English version:
Mathematical Notes, 1976, 19:2, 158–164

Bibliographic databases:

UDC: 513.8
Received: 21.02.1975

Citation: B. A. Koscheev, “Connectedness and solar properties of sets in normed linear spaces”, Mat. Zametki, 19:2 (1976), 267–278; Math. Notes, 19:2 (1976), 158–164

Citation in format AMSBIB
\Bibitem{Kos76}
\by B.~A.~Koscheev
\paper Connectedness and solar properties of sets in normed linear spaces
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 2
\pages 267--278
\mathnet{http://mi.mathnet.ru/mz7746}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=410208}
\zmath{https://zbmath.org/?q=an:0327.46026}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 2
\pages 158--164
\crossref{https://doi.org/10.1007/BF01098750}


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    Erratum
    • Errata
      Mat. Zametki, 1976, 19:6, 9521–952


    This publication is cited in the following articles:
    1. V. S. Balaganskii, L. P. Vlasov, “The problem of convexity of Chebyshev sets”, Russian Math. Surveys, 51:6 (1996), 1127–1190  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. A. R. Alimov, “Geometrical Characterization of Strict Suns in $\ell^\infty(n)$”, Math. Notes, 70:1 (2001), 3–10  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. R. Alimov, “On the Structure of the Complements of Chebyshev Sets”, Funct. Anal. Appl., 35:3 (2001), 176–182  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. A. R. Alimov, “The Geometric Structure of Chebyshev Sets in $\ell^\infty(n)$”, Funct. Anal. Appl., 39:1 (2005), 1–8  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. A. R. Alimov, “Connectedness of suns in the space $c_0$”, Izv. Math., 69:4 (2005), 651–666  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. A. R. Alimov, “Monotone path-connectedness of Chebyshev sets in the space $C(Q)$”, Sb. Math., 197:9 (2006), 1259–1272  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. A. R. Alimov, “Bounded strict solar property of strict suns in the space $C(Q)$”, Moscow University Mathematics Bulletin, 68:1 (2013), 14–17  mathnet  crossref
    8. A. R. Alimov, “Local solarity of suns in normed linear spaces”, J. Math. Sci., 197:4 (2014), 447–454  mathnet  crossref
    9. A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730  mathnet  crossref  mathscinet
    10. A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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