Topological Free Entropy Dimension for Approximately Divisible $C^*$-algebras

Abstract

Let $\mathcal{A}$ be a unital separable approximately divisible C$^*$-algebra. We show that $\mathcal{A}$ is generated by two self-adjoint elements and the topological free entropy dimension of any finite generating set of $\mathcal{A}$ is less than or equal to 1.