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

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Matematicheskie Zametki, 1976, Volume 19, Issue 2, Pages 267–278 (Mi mzm7746)

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

Full-text PDF (948 kB) Citations (10)

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.

Received: 21.02.1975

English version:
Mathematical Notes, 1976, Volume 19, Issue 2, Pages 158–164
DOI: https://doi.org/10.1007/BF01098750

Bibliographic databases:

UDC: 513.8

Language: Russian

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

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\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/mzm7746}

\mathscinet{http://mathscinet.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}

Linking options:

https://www.mathnet.ru/eng/mzm7746

https://www.mathnet.ru/eng/mzm/v19/i2/p267

Erratum

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

This publication is cited in the following 10 articles:

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
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
A. R. Alimov, “Bounded strict solar property of strict suns in the space $C(Q)$ ”, Moscow University Mathematics Bulletin, 68:1 (2013), 14–17
A. R. Alimov, “Local solarity of suns in normed linear spaces”, J. Math. Sci., 197:4 (2014), 447–454
A. R. Alimov, “Monotone path-connectedness of Chebyshev sets in the space $C(Q)$ ”, Sb. Math., 197:9 (2006), 1259–1272
A. R. Alimov, “The Geometric Structure of Chebyshev Sets in $\ell^\infty(n)$ ”, Funct. Anal. Appl., 39:1 (2005), 1–8
A. R. Alimov, “Connectedness of suns in the space $c_0$ ”, Izv. Math., 69:4 (2005), 651–666
A. R. Alimov, “Geometrical Characterization of Strict Suns in $\ell^\infty(n)$ ”, Math. Notes, 70:1 (2001), 3–10
A. R. Alimov, “On the Structure of the Complements of Chebyshev Sets”, Funct. Anal. Appl., 35:3 (2001), 176–182
V. S. Balaganskii, L. P. Vlasov, “The problem of convexity of Chebyshev sets”, Russian Math. Surveys, 51:6 (1996), 1127–1190

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

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