On the k-metric Dimension of Metric Spaces
  The metric dimension of a general metric space was defined in 1953, applied to the set of vertices of a graph metric in 1975, and developed further for metric spaces in 2013. It was then generalised in 2015 to the k-metric dimension of a graph for each positive integer k, where k=1 corresponds to the original definition. Here, we discuss the k-metric dimension of general metric spaces. 
A. F. Beardon and J. A. Rodriguez-Velazquez
math.MG