Inductive limits of semiprojective C*-algebras

We prove closure properties for the class of C*-algebras that are inductive limits of semiprojective C*-algebras. Most importantly, we show that this class is closed under shape domination, and so in particular under shape and homotopy equivalence. It follows that the considered class is quite large. It contains for instance the stable suspension of any nuclear C*-algebra satisfying the UCT and with torsion-free $K_0$-group. In particular, the stabilized C*-algebra of continuous functions on the pointed sphere is isomorphic to an inductive limit of semiprojectives.