On Topological Transitivity

Topological transitivity is an important property in the setting of discrete dynamical systems, as it represents a type of complex global behavior, which is equivalent to some kind of chaos. This necessitates the study of conditions ensuring transitivity for various systems. Such conditions, for maps on intervals, have been in [1], [2], [3] etc. Since it is not always possible to exhibit dense orbits, or to construct a topological Conjugacy with known topologically transitive maps, these results have acquired practical value. In the present work, we provide elementary proofs for some known results in this context, and also improve them.