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The Homotopy Lifting Theorem for Semiprojective $C^*$-Algebras

Bruce Blackadar


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.

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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