Continuities of metric projection and geometric consequences
type: Item
instance of: scholarly article
title: Continuities of metric projection and geometric consequences
zbMATH Open document ID: 0906.46011
author: Robert Huotari
author: Wu Li
published in: Journal of Approximation Theory
publication date: 1997-10-20T00:00:00Z
review text: This paper characterizes geometric structures (convexity, tabularity, and polyhedral structure) of a subset \(K\) of a normed linear space via different continuity conditions on the metric projection onto \(K\). In finite-dimensional spaces with the uniform norm, it is shown that convexity is equivalent to rotation-invariant almost convexity. Those sets every rotation of which have continuous metric projections are characterized.
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 1076157
zbMATH Keywords: convexity
zbMATH Keywords: geometric structures
zbMATH Keywords: tabularity
zbMATH Keywords: polyhedral structure
zbMATH Keywords: continuity conditions on the metric projection
zbMATH Keywords: rotation-invariant almost convexity
reviewed by: Joe Howard
MaRDI profile type: Publication
full work available at URL: jath.1996.3018
OpenAlex ID: W2074922302
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DOI: 10.1006/JATH.1996.3018
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description: scientific article; zbMATH DE number 1076157