The Homotopy Lifting Theorem for Semiprojective C^*-Algebras - Blackadar, Bruce (MATHEMATICA SCANDINAVICA, 2016)
We prove a complete analog of the Borsuk Homotopy Extension Theorem for arbitrary semiprojective C^*-algebras. We also obtain some other results about semiprojective C^*-algebras: a partial lifting theorem with specified quotient, a lifting result for homomorphisms close to a liftable homomorphism, and that sufficiently close homomorphisms from a semiprojective C^*-algebra are homotopic.