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Mat. Zametki, 1970, Volume 7, Issue 5, Pages 593–604 (Mi mz9543)  

This article is cited in 6 scientific papers (total in 6 papers)

Approximate properties of sets in Banach spaces

L. P. Vlasov

Sverdlovsk Branch, V. A. Steklov Mathematical Institute, Academy of Sciences of the USSR

Abstract: Various generalizations of the notion of “sun” are considered and connections among them are established. A series of results from works of the author on Chebyshev sets are restated in new terms. It is proved that a Chebyshev set with a continuous metric projection is convex in a smooth reflexive space.

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English version:
Mathematical Notes, 1970, 7:5, 358–364

Bibliographic databases:

UDC: 517.5
Received: 30.06.1969

Citation: L. P. Vlasov, “Approximate properties of sets in Banach spaces”, Mat. Zametki, 7:5 (1970), 593–604; Math. Notes, 7:5 (1970), 358–364

Citation in format AMSBIB
\Bibitem{Vla70}
\by L.~P.~Vlasov
\paper Approximate properties of sets in Banach spaces
\jour Mat. Zametki
\yr 1970
\vol 7
\issue 5
\pages 593--604
\mathnet{http://mi.mathnet.ru/mz9543}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=265849}
\zmath{https://zbmath.org/?q=an:0205.12302|0198.45903}
\transl
\jour Math. Notes
\yr 1970
\vol 7
\issue 5
\pages 358--364
\crossref{https://doi.org/10.1007/BF01123847}


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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. L. P. Vlasov, “Approximative properties of sets in normed linear spaces”, Russian Math. Surveys, 28:6 (1973), 1–66  mathnet  crossref  mathscinet  zmath
    2. 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
    3. I. G. Tsar'kov, “Properties of Sets Admitting Stable $\varepsilon$-Selections”, Math. Notes, 89:4 (2011), 572–576  mathnet  crossref  crossref  mathscinet  isi
    4. 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
    5. 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
    6. I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. Math., 80:2 (2016), 442–461  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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