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 Uspekhi Mat. Nauk, 1973, Volume 28, Issue 6(174), Pages 3–66 (Mi umn4976)

Approximative properties of sets in normed linear shaces

L. P. Vlasov

Abstract: This article presents results on Chebyshev sets and related questions. It is mainly concerned with proving the connectedness, “solarity” and convexity of Chebyshev sets and their generalizations under additional assumptions. Also considered are certain questions of approximative compactness, continuity of the metric projection, and various approximative-geometric properties of sets. We study the relationships between “suns” and conditions for the convexity of “suns”. Papers on the above topics are surveyed.

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English version:
Russian Mathematical Surveys, 1973, 28:6, 1–66

Bibliographic databases:

UDC: 519.9
MSC: 41A50, 46Bxx, 26B25, 18B30

Citation: L. P. Vlasov, “Approximative properties of sets in normed linear shaces”, Uspekhi Mat. Nauk, 28:6(174) (1973), 3–66; Russian Math. Surveys, 28:6 (1973), 1–66

Citation in format AMSBIB
\Bibitem{Vla73} \by L.~P.~Vlasov \paper Approximative properties of sets in normed linear shaces \jour Uspekhi Mat. Nauk \yr 1973 \vol 28 \issue 6(174) \pages 3--66 \mathnet{http://mi.mathnet.ru/umn4976} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=404963} \zmath{https://zbmath.org/?q=an:0291.41028|0293.41031} \transl \jour Russian Math. Surveys \yr 1973 \vol 28 \issue 6 \pages 1--66 \crossref{https://doi.org/10.1070/RM1973v028n06ABEH001624} 

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