Properties of monotone path-connected sets

DOI10.1070/IM8995zbMath1466.41017OpenAlexW3096567271MaRDI QIDQ4989080

I. G. Tsar'kov

Publication date: 20 May 2021

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

Full work available at URL: https://doi.org/10.1070/im8995

zbMATH Keywords

continuous selectionmetric projectionChebyshev setsunsolaritymonotone path-connected setMenger connected setspan (bar)

Mathematics Subject Classification ID

Selections in general topology (54C65) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Connected and locally connected spaces (general aspects) (54D05) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Related Items (11)

Uniformly and locally convex asymmetric spaces ⋮ Solarity and connectedness of sets in the space and in finite-dimensional polyhedral spaces ⋮ Monotone path-connectedness of strict suns ⋮ 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 ⋮ Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces ⋮ Density of the points of continuity of the metric function and projection in asymmetric spaces ⋮ Connectedness in asymmetric spaces ⋮ Sets in \(\mathbb{R}^n\) monotone path-connected with respect to some norm ⋮ On local properties of spaces implying monotone path-connectedness of suns ⋮ Properties of suns in the spaces \(L^1\) and \(C(Q)\)

Cites Work

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• Separation of convex sets by extreme hyperplanes
• New criteria for the existence of a continuous \(\epsilon\)-selection
• Die Metrische Struktur der Sonnen in \(l_{\infty}(n)\)
• Suns in normed linear spaces which are finite dimensional
• The connectivity and approximation properties of sets in linear normed spaces
• Continuous ε-selection
• Connectedness and solarity in problems of best and near-best approximation
• Local and global continuous $ \varepsilon$-selection
• Continuous selections for metric projection operators and for their generalizations
• Geometric Aspects of General Topology
• Approximative properties of sets and continuous selections
• Chebyshev centres, Jung constants, and their applications
• Topological Fixed Point Theory of Multivalued Mappings

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