Connectedness and other geometric properties of suns and Chebyshev sets

DOI10.1007/s10958-016-3000-1zbMath1361.46012OpenAlexW2513584590MaRDI QIDQ328734

I. G. Tsar'kov, Alexey R. Alimov

Publication date: 21 October 2016

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-016-3000-1

zbMATH Keywords

approximation theorynormed linear spacessuns

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (19)

A monotone path-connected set with outer radially lower continuous metric projection is a strict sun ⋮ Geometry of the singular set of hypersurfaces and the eikonal equation ⋮ Continuous \(\epsilon\)-selection and monotone path-connected sets ⋮ Continuous selections in asymmetric spaces ⋮ Continuous selections for metric projection operators and for their generalizations ⋮ Continuity of the metric projection and local solar properties of sets. Continuity of the metric projection and local solar properties of sets, continuity of the metric projection and solar properties ⋮ Continuous selection for set-valued mappings ⋮ Selections of the best and near-best approximation operators and solarity ⋮ Weakly monotone sets and continuous selection from a near-best approximation operator ⋮ Chebyshev sets with piecewise continuous metric projection ⋮ Selections of the metric projection operator and strict solarity of sets with continuous metric projection ⋮ Metric max-distance function in max-approximation problems ⋮ Convex analysis in normed spaces and metric projections onto convex bodies ⋮ Smoothness of solutions of the eikonal equation and regular points of their level surfaces ⋮ The geometry of a singular set of hypersurfaces and the eikonal equation ⋮ Approximative properties of sets and continuous selections ⋮ New criteria for the existence of a continuous \(\epsilon\)-selection ⋮ Smooth solutions of the eikonal equation and the behaviour of local minima of the distance function ⋮ Weakly monotone sets and continuous selection in asymmetric spaces

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