On some geometric properties of suns

DOI10.1016/0021-9045(74)90122-1zbMath0272.41020OpenAlexW2013378447MaRDI QIDQ2264280

Bruno Brosowski, Frank Deutsch

Publication date: 1974

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(74)90122-1

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (31)

A monotone path-connected set with outer radially lower continuous metric projection is a strict sun ⋮ Banach-Stone theorems for spaces of vector bundle continuous sections ⋮ Connectedness and other geometric properties of suns and Chebyshev sets ⋮ Best approximation in the space of continuous vector-valued functions ⋮ Lower semicontinuity, almost lower semicontinuity, and continuous selections for set-valued mappings ⋮ Suns, moons, and \(\mathring{B}\)-complete sets in asymmetric spaces ⋮ On Banach space properties that are not invariant under the Banach-Mazur distance 1 ⋮ Ein Abstiegsverfahren für Approximationsaufgaben in normierten Räumen ⋮ Isometries on the vector valued little Bloch space ⋮ 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 for the metric projection and alternation ⋮ A generalized ACK structure and the denseness of norm attaining operators ⋮ Isometries between generalized Nachbin weighted spaces: a Banach-Stone type theorem ⋮ Selections of the metric projection operator and strict solarity of sets with continuous metric projection ⋮ Strict protosuns in asymmetric spaces of continuous functions ⋮ Some new continuity concepts for metric projections ⋮ Extreme points in duals of operator spaces ⋮ Support cones and convexity of sets in ℝⁿ ⋮ Rethinking polyhedrality for Lindenstrauss spaces ⋮ Nonlinear weighted best simultaneous approximation in Banach spaces ⋮ Schnitte für die metrische Projektion ⋮ Extreme Point Methods and Banach-Stone Theorems ⋮ Generalized derivatives of distance functions and the existence of nearest points ⋮ Local solarity of suns in normed linear spaces ⋮ LINEAR SURJECTIVE ISOMETRIES BETWEEN VECTOR-VALUED FUNCTION SPACES ⋮ Anisotropic best τ_C -approximation in normed spaces ⋮ Characterizations and Uniqueness of Mutually Nearest Points for Two Sets in Normed Spaces ⋮ Extensions of linear operators from hyperplanes and strong uniqueness of best approximation in \(\mathcal{L}(X, W)\) ⋮ Radial continuity of set-valued metric projections ⋮ On continuity of metric projections ⋮ Polyhedral norms in an infinite dimensional space

Cites Work

• On the lower semicontinuity of the set-valued metric projection
• Continuity of the set-valued metric projection
• Charakterisierung bester Approximationen in normierten Vektorräumen
• On the rational Tschebyscheff operator
• Suns, moons, and quasi-polyhedra
• Sur un polynôme d'interpolation
• Topologies on Spaces of Subsets
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