Classification of simple C*-algebras: Inductive limits of matrix algebras over one-dimensional spaces

In this article, we will give a complete classification of simple C*-algebras which can be written as inductive limits of algebras of the form A(n) = circle plus(i-l)(kn) M-[n,M-i](C(X-n,X-i)), where X-n,X-i are arbitrary variable one-dimensional compact metrizable spaces. The results unity and generalize the previous results for the case X-n,X-i = S-l and for the case of X-n,X-i being trees. We obtain our classification results by reducing the case of general one-dimensional spaces to the case of circles. The techniques in this paper play important roles in the study of the case of higher-dimensional spaces. (C) 2002 Elsevier Science (USA).