1. The problem statement, all variables and given/known data Let (K, d) and (K', d') be two compact metric spaces and let f:K-->K' and g:K'--->K be isometries. Show that f(K)=K' and g(K')=K 2. Relevant equations n/a 3. The attempt at a solution I know that isometry implies that I can find one-to-one correspondence mapping, but not sure how to show both function and inverse function are subjective. Please help. Thanks!