Consider H to be a interval and f: H->H be a cts fxn.

For nontrivial closed intervals, suppose that U and V are contained in H, we can find m such that V contained in f^{m}(U).

Show that the periodic pts are dense in H.

I need to show that every point of H is the limit of some

sequence of points in H. Not sure where to proceed.

Show that f is topologically transitive.

f:H->H is topologically transitive if for all open sets U,V (non empty) there exists x in U and n such that f^{n}(x) in V. ie f^{n}(U) intersection V nonempty. Doesn't that just follow from assumption?