Cut points in metric spaces
type: Item
instance of: scholarly article
title: Cut points in metric spaces
zbMATH Open document ID: 1142.54007
author: Andreas W. M. Dress
author: Katharina T. Huber
author: Jack H. Koolen
author: Vincent Moulton
published in: Applied Mathematics Letters
publication date: 2008-05-21T00:00:00Z
review text: Inspired by the corresponding concept in graph theory, the authors define two apparently different notions of cut point in a metric space \((X,d)\) then show that they are actually the same. A function \(f:X\to\mathbb R\) is a virtual cut point if \(f(x)+f(y)\geq d(x,y)\) and supp\((f)\) splits into non-empty \(A\cup B\) with \(d(a,b)=f(a)+f(b)\) when \(a\in A\) and \(b\in B\), and is a topological cut point if it is in the tight span \(T(d)\) and \(T(d)\setminus\{f\}\) is a disconnected subspace of \(\mathbb R^X\). In both the abstract and the body of the paper the tight span is misdefined.
reviewed by: David B. Gauld
Mathematics Subject Classification ID: 54D05
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 5277559
zbMATH Keywords: tight span
zbMATH Keywords: cut point
zbMATH Keywords: metric space
zbMATH Keywords: block decomposition
zbMATH Keywords: optimal realization
MaRDI profile type: Publication
full work available at URL: j.aml.2007.05.018
OpenAlex ID: W2120321913
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DOI: 10.1016/J.AML.2007.05.018
description: scientific article; zbMATH DE number 5277559