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

• Autores: Bruce Blackadar
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 118, Nº 2, 2016, págs. 291-302
• Idioma: inglés
• DOI: 10.7146/math.scand.a-23691
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• Resumen

  • 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.