Metric completions of ordered groups and K0+of exchange rings

Abstract

We give a description of the closure of the natural a ne contin- uous function representation of K0(R) for any exchange ring R. This goal is achieved by extending the results of Goodearl and Handelman, about metric completions of dimension groups, to a more general class of pre-ordered groups, which includes K0 of exchange rings. As a consequence, the results about K+ 0 of regular rings, which the author gave in an earlier paper, can be extended to a wider class of rings, which includes C -algebras of real rank zero, among others. Also, the framework of pre-ordered groups developed here allows other potential applications.