On the metric dimension of certain metric manifolds
type: Item
instance of: scholarly article
title: On the metric dimension of certain metric manifolds
zbMATH Open document ID: 1475.54019
author: Majid Heydarpour
author: S. Maghsoudi
published in: Bulletin of the Iranian Mathematical Society
publication date: 2021-08-02T00:00:00Z
review text: Recall that the metric dimension, \(\mathrm{md}(X)\) of a metric space \((X,d)\) is the minimal cardinality of a resolving set, i.e. a non-empty set \(A\subset X\) such that for any \(x,y\in X\), if \(d(x,a)=d(y,a)\) for all \(a\in X\) then \(x=y\). If \((X,d)\) is an \(n\)-dimensional geometric space and \(N\subset X\) an \((n-1)\)-dimensional submanifold without boundary then \(n\le \mathrm{md}(N)\le n+1\). If \((M,d)\) is an \(n\)-dimensional geometric manifold with boundary then \(n\le \mathrm{md}(\partial M)\le \mathrm{md}(M)\le \mbox{md}(\mathrm{int}M)=n+1\).
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 51K05
zbMATH DE Number: 7377327
zbMATH Keywords: metric dimension
zbMATH Keywords: resolving set
zbMATH Keywords: geometric manifolds with boundary
zbMATH Keywords: geometric spaces
zbMATH Keywords: Riemannian manifold
reviewed by: David B. Gauld
MaRDI profile type: Publication
full work available at URL: s41980-020-00404-7
OpenAlex ID: W3035167145
cites work: BISECTORS IN VECTOR GROUPS OVER INTEGERS
cites work: The metric dimension of metric spaces
cites work: The Local metric dimension of the lexicographic product of graphs
cites work: Q3310101
cites work: On the k-metric dimension of metric spaces
cites work: Q5818996
cites work: Determining sets, resolving sets, and the exchange property
cites work: On the metric dimension of infinite graphs
cites work: Q3070331
cites work: Is it possible to determine a point lying in a simplex if we know the distances from the vertices?
cites work: Q4119237
cites work: On metric orbit spaces and metric dimension
cites work: The metric dimension of geometric spaces
cites work: THE METRIC DIMENSION OF METRIC MANIFOLDS
cites work: Landmarks in graphs
cites work: Introduction to Smooth Manifolds
cites work: Q4384481
cites work: Metric bases in digital geometry
cites work: Q4314293
cites work: Lexicographic metric spaces: Basic properties and the metric dimension
cites work: Q4075485
DOI: 10.1007/S41980-020-00404-7
description: scientific article; zbMATH DE number 7377327