However, a uniformly continuous function on a general metric space admits a concave modulus of continuity if and only if the ratios are uniformly bounded for all pairs bounded away from the diagonal of.

However, a uniformly continuous function on a general metric space admits a concave modulus of continuity if and only if the ratios are uniformly bounded for all pairs bounded away from the diagonal of ; this condition is certainly satisfied by any bounded uniformly continuous function ; hence in particular, by any continuous function on a compact metric space.

0.003 seconds.