I was reading this [post][1] and wondered.  Does there exist a topologically transitive (TT) map $f:\mathbb{R}^n\to\mathbb{R}^n$ when $n\geq 2$?  I know that post asks for compactness and topological mixing(ness) but if we relax the requirement to only TT is it possible?

Note: If $\mathbb{R}^n$ is replaced by an infinite-dimensional Hilbert space, then the Ansari-Bernal theorem guarantees such a map much exist moreover it must be linear... So maybe it can exist in the finite-dimensional case?


  [1]: https://mathoverflow.net/questions/336489/existence-of-topologically-mixing-discrete-dynamical-system-on-manifold