Monotone path-connectedness of Chebyshev sets in three-dimensional spaces

DOI10.1070/SM9325zbMath1472.41019OpenAlexW3134786524MaRDI QIDQ5003310

Borislav Borisovich Bednov, Alexey R. Alimov

Publication date: 21 July 2021

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm9325

zbMATH Keywords

Chebyshev setSuncylindrical normmonotone path-connected set

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Convex sets in topological linear spaces; Choquet theory (46A55)

Related Items (8)

Finite-dimensional spaces where the class of Chebyshev sets coincides with the class of closed and monotone path-connected sets ⋮ Suns, moons, and \(\mathring{B}\)-complete sets in asymmetric spaces ⋮ Monotone path-connectedness of strict suns ⋮ \(\mathring{B}\)-complete sets: approximative and structural properties ⋮ Solarity and proximinality in generalized rational approximation in spaces \(C(Q)\) and \(L^p\) ⋮ Three-dimensional spaces where all bounded Chebyshev sets are monotone path connected ⋮ On local properties of spaces implying monotone path-connectedness of suns ⋮ Ball-complete sets and solar properties of sets in asymmetric spaces

Cites Work

• Convex functions, monotone operators and differentiability.
• Suns in normed linear spaces which are finite dimensional
• 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)$
• Continuous selections for metric projection operators and for their generalizations
• Convexity of Chebyshev sets with respect to tangent directions
• Approximative properties of sets and continuous selections
• Weakly monotone sets and continuous selection in asymmetric spaces
• Preservation of approximative properties of subsets of Chebyshev sets and suns in $ \ell^\infty (n)$
• Convex Sets and Chebyshev Sets II.
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