On the metric dimension of certain metric manifolds
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 \(n\le \mathrm{md}(\partial M)\le \mathrm{md}(M)\le \mbox{md}(\mathrm{int}M)=n+1\).
scientific article; zbMATH DE number 7377327
scientific article