The metric dimension of geometric spaces (Q471461)

Given a metric space, \((X,d)\), one calls a subset, \(A\), a resolving set if the map \(x\mapsto\langle d(x,a)\rangle_{a\in A}\) is injective. The metric dimension, \(\text{md}(X,d)\), of the space is the minimum cardinality of a resolving set. The authors prove that for all connected homogeneous Riemannian manifolds the metric dimension exceeds the manifold dimension by \(1\).