 Using this distance, the class of all (isometry classes of) compact metric spaces becomes a metric space in its own right.If formula_141 are metric spaces, and "N" is the Euclidean norm on "Rn", then formula_142 is a metric space, where the product metric is defined by

and the induced topology agrees with the product topology.By the equivalence of norms in finite dimensions, an equivalent metric is obtained if "N" is the taxicab norm, a p-norm, the maximum norm, or any other norm which is non-decreasing as the coordinates of a positive "n"-tuple increase (yielding the triangle inequality).