The metric dimension of geometric spaces

For a metric space (X,d)(X,d), a subset A   resolves (X,d)(X,d) if each point x∈Xx∈X is uniquely determined by the distances d(x,a)d(x,a) for a∈Aa∈A. Also the metric dimension of (X,d)(X,d) is the smallest cardinality md(X)md(X) such that there is a set A   of the cardinality md(X)md(X) that resolves X  . In this work we are going to compute md(X)md(X) for the case that X is an n-dimensional geometric space. This category includes a vast domain of Riemannian manifolds.