When the two metrics d_1,d_2 are those induced by norms \|\cdot \|_A, \|\cdot\|_B respectively, then strong equivalence is equivalent to the condition that, for all x \in X, .
In finite dimensional spaces, all metrics induced by the p-norm, including the euclidean metric, the taxicab metric, and the Chebyshev distance, are strongly equivalent [REF].