Approximate Homotopy of Homomorphisms from C(X) into a Simple C -algebra

Provides a proof of Generalized Homotopy Lemmas. These type of results play an important role in the classification theory of $*$-homomorphisms up to asymptotic unitary equivalence. Coverage includes the basic homotopy lemma for higher dimensional spaces; purely infinite simple $C^*$-algebras; approximate homotopy; and super homotopy.