Two metrics g_1 and g_2 defined on a space X are called equivalent if they induce the same metric topology on X. This is the case iff, for every point x_0 of X, every ball with center at x_0 defined with respect to g_1: B(x_0, r_1 ;g_1) = {x element X|g_1(x_0, x)

metric | metric equivalence problem | product metric