Diametrically Maximal and Constant Width Sets in Banach Spaces

DOI10.4153/CJM-2006-033-1zbMath1110.52003OpenAlexW2081214003MaRDI QIDQ3413540

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Publication date: 12 December 2006

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4153/cjm-2006-033-1

zbMATH Keywords

Hilbert spaceBanach spacecomplete setsbodies of constant widthdiametrically maximal setJune constantspherical intersection property

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Convex sets without dimension restrictions (aspects of convex geometry) (52A05)

Related Items (24)

Minkowski concentricity and complete simplices ⋮ Behaviour of inradius, circumradius, and diameter in generalized Minkowski spaces ⋮ Diametrically complete sets in Minkowski spaces ⋮ Complete sets in normed linear spaces ⋮ Porosity and unique completion in strictly convex spaces ⋮ Diametrically complete sets with empty interior and constant width sets with empty interior ⋮ Infinite-dimensional hyperspaces of convex bodies of constant width ⋮ Diametral points and diametral pairs in Banach spaces ⋮ Diametrically complete sets and normal structure ⋮ Some geometry of convex bodies in \(C(K)\) spaces ⋮ Porosity and diametrically maximal sets in \(C(K)\) ⋮ Renormings of nonseparable reflexive Banach spaces and diametrically complete sets with empty interior ⋮ Schauder bases and diametrically complete sets with empty interior ⋮ Normal structure and orbital fixed point conditions ⋮ The asymmetry of complete and constant width bodies in general normed spaces and the Jung constant ⋮ Convex values and Lipschitz behavior of the complete hull mapping ⋮ Densely ball remotal subspaces of \(C(K)\) ⋮ Intersection properties of polyhedral norms ⋮ Existence of diametrically complete sets with empty interior in reflexive and separable Banach spaces ⋮ Porosity and diametrical completeness ⋮ Thin sets of constant width ⋮ Complete sets need not be reduced in Minkowski spaces ⋮ On the equivalence of Aumann and Herer expectations of random sets ⋮ Semicontinuous functions and convex sets inC(K)spaces

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