Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces

DOI10.1070/IM2014v078n04ABEH002702zbMath1303.41018arXiv1312.4338MaRDI QIDQ2925758

Alexey R. Alimov

Publication date: 17 October 2014

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

Full work available at URL: https://arxiv.org/abs/1312.4338

zbMATH Keywords

cell-like setMenger convexityacyclic setsunCech homologymonotone path-connected setd-convexityMenger connectednessRainwater-Simons theorem

Mathematics Subject Classification ID

Axiomatic and generalized convexity (52A01) Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (17)

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 ⋮ Continuity of the metric projection and local solar properties of sets. Continuity of the metric projection and local solar properties of sets, continuity of the metric projection and solar properties ⋮ Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces ⋮ Selections of the best and near-best approximation operators and solarity ⋮ 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 ⋮ Approximative properties of sets and continuous selections ⋮ New criteria for the existence of a continuous \(\epsilon\)-selection ⋮ 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 ⋮ Unnamed Item ⋮ Weakly monotone sets and continuous selection in asymmetric spaces ⋮ Monotone path-connectedness of Chebyshev sets in three-dimensional spaces

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