Let be a continuous map on an interval I. Prove that f is topologically transitive and Perf is dense in I if and only if for each pair of open intervals and in I, there exists a periodic point and...

Let

be a continuous map on an interval I. Prove that f is topologically transitive and Perf is dense in I if and only if for each pair of open intervals

and

in I, there exists a periodic point

and a nonnegative integer k such that