Maximum product metric
= Maximum product metric
{title2=$D((x,x'),(y,y'))=\max\{d(x,y),d'(x',y')\}$}
The displayed metric on a product of two <metric spaces> satisfies its <triangle inequality> because $\max\{a+c,b+d\}\le\max\{a,b\}+\max\{c,d\}$ for nonnegative coordinates. Its open balls are products of equal-radius balls, so it induces the <product topology>.