Geometric structure of Chebyshev sets and suns in three-dimensional spaces with a cylindrical norm

DOI10.3103/S0027132220050022zbMath1465.41011OpenAlexW3137595392MaRDI QIDQ2027882

Alexey R. Alimov

Publication date: 28 May 2021

Published in: Moscow University Mathematics Bulletin (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s0027132220050022

zbMATH Keywords

polyhedral normChebyshev setsuncylindrical normmonotone path-connected set

Mathematics Subject Classification ID

Convex sets in (3) dimensions (including convex surfaces) (52A15) Topology of special sets defined by functions (54C50) Approximations and expansions (41A99)

Cites Work

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• Continuity of the metric projection, structural and approximate properties of sets
• Suns in normed linear spaces which are finite dimensional
• Preservation of approximative properties of Chebyshev sets and suns in a plane
• The geometric structure of Chebyshev sets in \(\ell^\infty(n)\)
• Connectedness and solarity in problems of best and near-best approximation
• Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces
• Monotone path-connectedness of Chebyshev sets in the space $ C(Q)$
• Selections of the metric projection operator and strict solarity of sets with continuous metric projection
• Convexity of Chebyshev sets with respect to tangent directions
• Chebyshev centres, Jung constants, and their applications
• Weakly monotone sets and continuous selection in asymmetric spaces
• Preservation of approximative properties of subsets of Chebyshev sets and suns in $ \ell^\infty (n)$

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