The Topological Markov Chain-Transitivity and Mixing

In this paper, we have discussed the one sided topological Markov chain and proved the following conditions to be equivalent: 1. topologically strongly mixing, 2 topologically weakly mixing, 3. topological transitivity and the existence of two periods which are co-prime. As a consequence, we have come to the conclusion that mixing implies positive entropy but the converse is not true.