Abstract
Let A A be a unital simple A H AH -algebra with real rank zero. It is shown that if A A satisfies a so-called fundamental comparison property, then A A has tracial topological rank zero. Combining some previous results, it is shown that a unital simple A H AH -algebra with real rank zero, stable rank one and weakly unperforated K 0 ( A ) K_0(A) must have slow dimension growth.
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