Multiplicity of topological systems

We define the topological multiplicity of an invertible topological system $(X,T)$ as the minimal number $k$ of real continuous functions $f_1,\cdots ,f_k$ such that the functions $f_i\circ T^n$, $n\in \mathbb{Z}$, $1\le i\le k,$ span a dense linear vector space in the space of real continuous functions on $X$ endowed with the supremum norm. We study some properties of topological systems with finite multiplicity. After giving some examples, we investigate the multiplicity of subshifts with linear growth complexity.