Traces and simple C^*-algebras with tracial topological rank zero

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Classification of homomorphisms and dynamical systems (2004, background): “Consequently, by [ 42 ], they have tracial topological rank zero.”
Classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras (2014, background): “9 of [52], there is a projection P ∈ J and a unital homomorphism ψ0 : B → (1− P )C2(1− P ) such that ‖PΨ(af )−Ψ(af )P‖ < ε0/8 and ‖Ψ(af )− [PΨ(af )P + ψ0 ◦ πJ ◦Ψ(af )]‖ < ε0/8 (e 5.”
A classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras, I: $C^*$-algebras with generalized tracial rank one. (2018, methodology): “7 of [57] and keep the notation in the proof of Lemma 4.”
Approximate Homotopy of Homomorphisms from C(x) Into a Simple C*-Algebra (2006, background): “We refer the reader to [24], [28], [25], [27], [3], [45] and [46] for more information.”
On the Classification of Simple Z‐Stable C*‐Algebras with Real Rank Zero and Finite Decomposition Rank (2005, result): “. (The decomposition rank is a notion of covering dimension for nuclear C∗-algebras introduced in [7] by E. Kirchberg and the author; cf. also [21] and [22].) Similar results were obtained in [2] and [11], under the additional assumption that the algebras have only countably many extremal tracial st”