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Let $A$ be a simple separable unital locally approximately subhomogeneousC*-algebra (locally ASH algebra). It is shown that $A\otimes Q$ can betracially approximated by unital Elliott-Thomsen algebras with trivial$\textrm{K}_1$-group, where $Q$ is the universal UHF algebra. In particular, itfollows that $A$ is classifiable by the Elliott invariant if $A$ is Jiang-Sustable.

The classification of simple separable unital locally ASH algebras