Geodesic
Approximative properties of sets in normed linear spaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 28 (1973) no. 6, pp. 1-66

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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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     author = {L. P. Vlasov},
     title = {Approximative properties of sets in normed linear spaces},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     number = {6},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_1973_28_6_a0/}
}
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L. P. Vlasov. Approximative properties of sets in normed linear spaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 28 (1973) no. 6, pp. 1-66. http://geodesic.mathdoc.fr/item/RM_1973_28_6_a0/