I'm cross-posting this from SE.

Let $T$ be a group, and let $(X,T)$ be a flow, i.e. $X$ is a compact Hausdorff space and $T$ acts on $X$ by homeomorphisms. A flow $X$ is called topologically transitive if for any open $U,V⊆X$ there is $t∈T$ with $tU\cap V\neq\emptyset$, and $X$ is called pointwise minimal if for any $x∈X$, the orbit closure $\overline{Tx}$ is a minimal flow.

It is known (I think due to Ellis) that if $T$ is countable, then any flow $X$ which is both topologically transitive and pointwise minimal is in fact minimal. My question is about if $T$ is uncountable. Are there examples of flows which are topologically transitive, point-wise minimal, and not minimal?

minimalflow? $\endgroup$ – Sebastian Goette Jan 12 '16 at 17:48