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In mathematics the Assouad–Nagata dimension (or Nagata dimension) of a metric space is defined as the infimum of all integers such that: There exists a constant such that for all the space has a -bounded covering with -multiplicity at most . Here -bounded means that the diameter of each set of the covering is bounded by , and -multiplicity is the infimum of integers such that each point belongs to at most members of the covering.[1]