Given a metric space $X$ of dimension $d$ it is a classical fact that the minimal $n$ that guarantees that $X$ can be embedded in $[0,1]^{n}$, is $n=2d+1$. An analogous problem in the category of dynamical systems, is under what conditions one can guarantee that the metric topological system $(X,T)$ is embeddable in $([0,1]^{n})^{\mathbb{Z},shift}$. The embedding is induced by $n$ real continuous functions on $X$, so this question can also be thought as a topological dynamical analogue of the Krieger Generator Theorem. A well known theorem by Jaworski states that if $(X,T)$ is aperiodic and $X$ is finite dimensional then $n=1$ is sufficient. I will discuss several generalizations of this theorem to the infinite-dimensional setting and explain a connection to the Bonatti-Crovisier Topological Tower Theorem.