  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.
