semigroup may not be itself Abelian, all of its transformations commutes with any homeomorphism coming from the action.

The Ellis semigroup construction is functorial (covariant) in the sense that any onto continuous and $T$-equivariant mapping $\pi : \mathbb{X} \twoheadrightarrow \mathbb{Y}$ gives rise to an onto continuous semigroup morphism $\pi ^*: E(\mathbb{X},T) \twoheadrightarrow E(\mathbb{Y},T)$, satisfying $\pi (x.g)=\pi (x).\pi ^*(g)$ for any $x\in \mathbb{X}$ and any transformation $g\in E(\mathbb{X},T)$. Here we have written $x.g$ for the evaluation of a mapping $g$ at a point $x$. With this convention the Ellis semigroup is always a compact right-topological semigroup, that is, if some net $( h_\lambda )$ converges pointwise to $h$ then the net $( g.h_\lambda ) $ converges pointwise to $g.h$ for any $g$, where $g.h$ stands for the composition map which at each point $x$ reads $(x.g).h$.

Among the whole category of dynamical systems, the certainly most simple objects are the *equicontinuous dynamical systems*. These are the dynamical systems such that the family of homeomorphisms coming from the group action is equicontinous, and within the more specific class of compact minimal dynamical systems they exactly shows up as the well known class of *Kronecker systems*. About these particular dynamical systems one has 