Approximatively compact sets in asymmetric Efimov-Stechkin spaces and convexity of almost suns

DOI10.1134/S0001434621110316zbMath1489.41020OpenAlexW4200239601MaRDI QIDQ2063686

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

Publication date: 11 January 2022

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434621110316

zbMATH Keywords

asymmetric normed spacesunasymmetric Efimov-Stechkin spaceprotosununimodal set

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 (6)

Continuity of a metric function and projection in asymmetric spaces ⋮ Suns, moons, and \(\mathring{B}\)-complete sets in asymmetric spaces ⋮ \(\mathring{B}\)-complete sets: approximative and structural properties ⋮ Estimates of the Chebyshev radius in terms of the MAX-metric function and the MAX-projection operator ⋮ Unnamed Item ⋮ Ball-complete sets and solar properties of sets in asymmetric spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Relations between certain classes of sets in Banach spaces
• Efimov-Stechkin spaces
• The connectivity and approximation properties of sets in linear normed spaces
• Differentiability of distance function and the proximinal condition implying convexity
• Geometric properties of Banach spaces and the existence of nearest and farthest points
• Connectedness and solarity in problems of best and near-best approximation
• Functional Analysis in Asymmetric Normed Spaces
• The Banach-Mazur theorem for spaces with an asymmetric distance
• Separation axioms and covering dimension of asymmetric normed spaces
• Weakly monotone sets and continuous selection in asymmetric spaces

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