Published online by Cambridge University Press: 04 May 2017
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 an
$n$-dimensional compactum supporting a weakly mixing completely scrambled homeomorphism. This solves a 15-year-old open problem.