Metrics defined via discrepancy functions
type: Item
instance of: scholarly article
title: Metrics defined via discrepancy functions
zbMATH Open document ID: 1120.54008
author: Matt Insall
author: Włodzimierz J. Charatonik
published in: Topology and its Applications
publication date: 2007-05-10T00:00:00Z
review text: In this paper the authors introduce the notion of a discrepancy function. A discrepancy function is a real extended, non-negative function \(\omega\) defined on certain pairs \((A,U)\) (where \(A\subset U\)) of subsets of a set \(X\) with the property that, for fixed \(A\), the function \(\omega\) takes arbitrarily small values as \(U\) varies. They present a number of natural examples of discrepancy functions and show how they can be used to define traditional pseudo-metrics, quasimetrics and metrics on hyperspaces of topological spaces and measure spaces.
reviewed by: Alejandro Illanes
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54E99
zbMATH DE Number: 5151654
zbMATH Keywords: Discrepancy Functions
zbMATH Keywords: Hyperspace
zbMATH Keywords: Metric
zbMATH Keywords: Pseudometric
zbMATH Keywords: Quasimetric
zbMATH Keywords: Symmetric
zbMATH Keywords: Whitney Map
MaRDI profile type: Publication
full work available at URL: j.topol.2006.12.008
OpenAlex ID: W2089762558
cites work: A Metric on Hyperspaces Defined by Whitney Maps
cites work: Fixed points for pairs of mappings in d-complete topological spaces
cites work: Q4230677
cites work: Q4340906
DOI: 10.1016/J.TOPOL.2006.12.008
description: scientific article; zbMATH DE number 5151654