Mixing completely scrambled system exists
  We prove that there exists a topologically mixing homeomorphism which is completely scrambled. We also prove that for any integer $n\geq 1$ there is a continuum of topological dimension $n$ supporting a transitive completely scrambled homeomorphism, and $n$-dimensional compactum supporting a weakly mixing completely scrambled homeomorphism. This solves a 15 year old open problem. 
Jan P. Boro\'nski, Ji\v{r}\'i Kupka, Piotr Oprocha
math.DS