Suns in normed linear spaces which are finite dimensional

DOI10.1007/BF01456192zbMath0607.41027OpenAlexW2051648759MaRDI QIDQ1085364

Aldric L. Brown

Publication date: 1987

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164308

zbMATH Keywords

suns(BM)-spacesM-connected sets

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (21)

Characterisations of Chebyshev sets in \(c_{0}\) ⋮ Connectedness and other geometric properties of suns and Chebyshev sets ⋮ Solarity and connectedness of sets in the space and in finite-dimensional polyhedral spaces ⋮ Continuous \(\epsilon\)-selection and monotone path-connected sets ⋮ Monotone path-connectedness of strict suns ⋮ Separation of convex sets by extreme hyperplanes ⋮ Monotone path-connectedness of \(R\)-weakly convex sets in the space \(C(Q)\) ⋮ Weakly monotone sets and continuous selection from a near-best approximation operator ⋮ Selections of the metric projection operator and strict solarity of sets with continuous metric projection ⋮ Convex analysis in normed spaces and metric projections onto convex bodies ⋮ Existence, uniqueness, and stability of best and near-best approximations ⋮ On local properties of spaces implying monotone path-connectedness of suns ⋮ Properties of suns in the spaces \(L^1\) and \(C(Q)\) ⋮ Geometric structure of Chebyshev sets and suns in three-dimensional spaces with a cylindrical norm ⋮ Properties of monotone connected sets ⋮ Local solarity of suns in normed linear spaces ⋮ Unnamed Item ⋮ Properties of monotone path-connected sets ⋮ Monotone path-connectedness of Chebyshev sets in three-dimensional spaces ⋮ The geometry of Minkowski spaces -- a survey. II. ⋮ The geometric structure of Chebyshev sets in \(\ell^\infty(n)\)

Cites Work

• Die Metrische Struktur der Sonnen in \(l_{\infty}(n)\)
• A Representation Theorem for Bounded Convex Sets
• APPROXIMATIVE PROPERTIES OF SETS IN NORMED LINEAR SPACES
• Characterisation of normed linear spaces with Mazur's intersection property
• Fixed Point Theorems for Multi-Valued Transformations
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