Let $X$ be a compact metric space with a homeomorphism $f$· The dynamical system transitive, but not minimal. Also Let $Intran(f)$ be the set of all points whose orbit is not transitive. How to show that $Intran(f)$ is dense in $X$?
I have tried by contradiction. If that happens maybe both the the set of transitive orbits is open and also is the set of intransitive sets is open? Then there could be no two disjoint invariant open sets. I have also tried showing that the set of all transitive points is a Baire set, but it didn't work out, also. Any help would be good!