Properties of suns in the spaces \(L^1\) and \(C(Q)\)

DOI10.1134/S1061920821030122zbMath1487.41042OpenAlexW3200026388MaRDI QIDQ2239366

I. G. Tsar'kov

Publication date: 3 November 2021

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1061920821030122

zbMATH Keywords

metric projectionChebyshev setsunsolaritymonotone path-connected setMenger connected set

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Banach spaces of continuous, differentiable or analytic functions (46E15)

Related Items (8)

Suns, moons, and \(\mathring{B}\)-complete sets in asymmetric spaces ⋮ \(\mathring{B}\)-complete sets: approximative and structural properties ⋮ Solarity and proximinality in generalized rational approximation in spaces \(C(Q)\) and \(L^p\) ⋮ Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces ⋮ Chebyshev sets with piecewise continuous metric projection ⋮ On local properties of spaces implying monotone path-connectedness of suns ⋮ Properties of Chebyshev generalized rational fractions in \(L_1\) ⋮ Ball-complete sets and solar properties of sets in asymmetric spaces

Cites Work

• Unnamed Item
• Die Metrische Struktur der Sonnen in \(l_{\infty}(n)\)
• Suns in normed linear spaces which are finite dimensional
• Connectedness and solarity in problems of best and near-best approximation
• Local and global continuous $ \varepsilon$-selection
• Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces
• Properties of monotone path-connected sets

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