Chebyshev foam
type: Item
instance of: scholarly article
title: Chebyshev foam
zbMATH Open document ID: 0994.52006
DOI: 10.1016/S0166-8641(98)00033-9
author: Gordon G. Johnson
published in: Topology and its Applications
publication date: 2002-09-24T00:00:00Z
review text: Let \(E\) be the union of all finite-dimensional Euclidean spaces equipped with the natural norm and real inner product. A closed set \(C\subset E\) is a Chebyshev set if every point in \(E\) has a unique nearest point in \(C\). The construction of a Chebyshev set \(F\subset E\) with the following properties (Chebyshev foam) is presented in this paper: \(E\setminus F\) is dense in \(E\), \(E\setminus F\) has infinitely many components, every component of \(E\setminus F\) is bounded and the infimum of the diameters of the components of \(E\setminus F\) is 0.
Mathematics Subject Classification ID: 52A27
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 52A07
zbMATH DE Number: 1317229
zbMATH Keywords: Chebyshev set
zbMATH Keywords: metric space
zbMATH Keywords: pre-Hilbert space
zbMATH Keywords: convex set
reviewed by: Thomas V. Tonev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1317229