  In ergodic theory, given sufficient conditions on the system, every weak
mixing $\mathbb{N}$-action is strong mixing along a density one subset of
$\mathbb{N}$. We ask if a similar statement holds in topological dynamics with
density one replaced with thickness. We show that given sufficient initial
conditions, a group action in topological dynamics is strong mixing on a thick
subset of the group if and only if the system is $k$-transitive for all $k$,
and conclude that an analogue of this statement from ergodic theory holds in
topological dynamics when dealing with abelian groups.
