Un problème de connectivité sur les espaces métriques
type: Item
instance of: scholarly article
title: Un problème de connectivité sur les espaces métriques
zbMATH Open document ID: 0551.05050
DOI: 10.1016/S0195-6698(84)80007-4
published in: European Journal of Combinatorics
publication date: 1984-01-01T00:00:00Z
review text: If x and y are two points of a compact metric space E, we call connectivity in E between x and y the smallest number of points other than x or y that we must withdraw from E in order to get a metric space which does not admit any continuous path between x and y. We denote this number by \(C_ E(x,y)\) and we prove, under some regularity conditions on E, that if \(C_ E(x,y)<\infty\), then there exists in E a system of \(C_ E(x,y)\) innerly disjoint continuous paths between x and y. This result provides us with an extension of Menger's theorem for finite graphs and we show how it may become incorrect when E presents some kinds of irregularities.
reviewed by: M.Marx
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 54D05
zbMATH DE Number: 3877228
zbMATH Keywords: connectivity between points
zbMATH Keywords: Menger's theorem
zbMATH Keywords: compact metric space
author: Alain Quilliot
MaRDI profile type: Publication
cites work: Q5615282
cites work: Parallel concepts in graph theory
full work available at URL: s0195-6698(84)80007-4
OpenAlex ID: W2055164697
description: scientific article; zbMATH DE number 3877228