Classification of C∗-homomorphisms from C0(0, 1] to a C∗-algebra

A class of C∗-algebras is described for which the C∗-homomorphisms from C0(0, 1] to the algebra may be classified by means of the Cuntz semigroup functor. Examples are given of algebras—simple and nonsimple— for which this classification fails. It is shown that a suitable suspension of the Cuntz semigroup functor deals successfully with some of these counterexamples. © 2009 Elsevier Inc. All rights reserved.