Connectedness and solarity in problems of best and near-best approximation

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.
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