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 An=⊕i=1knM[n,i](C(Xn,i)), where Xn,i are arbitrary variable one-dimensional compact metrizable spaces. The results unify and generalize the previous results for the case Xn,i=S1 and for the case of Xn,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.