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.
\Bibitem{Vla73}
\by L.~P.~Vlasov
\paper Approximative properties of sets in normed linear spaces
\jour Russian Math. Surveys
\yr 1973
\vol 28
\issue 6
\pages 1--66
\mathnet{http://mi.mathnet.ru/eng/rm4976}
\crossref{https://doi.org/10.1070/RM1973v028n06ABEH001624}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=404963}
\zmath{https://zbmath.org/?q=an:0291.41028|0293.41031}
Linking options:
https://www.mathnet.ru/eng/rm4976
https://doi.org/10.1070/RM1973v028n06ABEH001624
https://www.mathnet.ru/eng/rm/v28/i6/p3
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