Let be $M$ a topological space, and $f: M\to M$ a dynamical system, i.e, a continuous map between from $M$ to $M$.
We say that a dynamical system, $f:M\to M$ is topologically transitive when, exists $x\in M$ such that, $Orb(x)=\{x,f(x),\ldots, f^n(x),\ldots\}$ is dense in $M.$
There is a problem in the book of Brin Stuck, An introduction to Dynamical Systems, that makes the following question: Is the product of two topologically transitive (minimal, topologically mixing) systems topologically transitive (minimal, topologically mixing)?
I already know that for minimal systems the answer is no, And as for mixing systems, the answer is yes.
But I have no intuition for the case of topologically transitive systems, so my question is:
Is the product of two topologically transitive maps, topologically transitive?