2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59467Let X be a locally compact space, and let A and B be Co(X)-algebras. We define the notion of an asymptotic Co(X)-morphism from A to B and construct representable E-theory groups RE(X;A,B). These are the universal groups on the category of separable Co(X)-algebras that are Co(X)-stable, Co(X)-homotopy-invariant, and half-exact. If A is RKK(X)-nuclear, these groups are naturally isomorphic to Kasparov's representable KK-theory groups RKK(X;A,B). Applications and examples are also discussed.For journal version, see http://www.idealibrary.com/links/doi/10.1006/jfan.2000.3654Operator AlgebrasK-Theory and Homology19K35 (primary) 46L80 (Secondary)text