Classification of homomorphisms from C () to a C^*-algebra

Let be a compact subset of C and let A be a unital simple, separable C^*-algebra with stable rank one, real rank zero and strict comparison. We show that, given a Cu-morphism: Cu (C () ) Cu (A) with (1_) 1A, there exists a homomorphism: C () A such that Cu () = and is unique up to approximate unitary equivalence. We also give classification results for maps from a large class of C^*-algebras to A in terms of the Cuntz semigroup.