Geodesic
Connectedness and solarity in problems of best and near-best approximation
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 71 (2016) no. 1, pp. 1-77

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This survey is concerned with structural characteristics of ‘suns’ in normed linear spaces, with special emphasis on connectedness and monotone path-connectedness. Consideration is given to both direct theorems in geometric approximation theory in which approximative properties of sets are derived from their structural characteristics, and converse theorems in which structural properties of sets are derived from their approximative characteristics. Geometric methods of approximation theory are employed in solving the eikonal equation. Bibliography: 231 titles.
Keywords: sun, strict sun, Chebyshev set, near-best approximation, connectedness, infinite connectedness, monotone path-connectedness
Mots-clés : eikonal equation. 
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A. R. Alimov; I. G. Tsar'kov. Connectedness and solarity in problems of best and near-best approximation. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 71 (2016) no. 1, pp. 1-77. http://geodesic.mathdoc.fr/item/RM_2016_71_1_a0/