2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63059In this paper I show that pointwise bounded asymptotic morphisms between separable metrisable locally convex *-algebras induce continuous maps between the quasi-unitary groups of the algebras, provided that the algebras support a certain amount of functional calculus. This links the asymptotic morphisms directly to Thomsen's non-stable definition of k-theory in the C* algebra case. A result on composition of asymptotic morphisms is also given.LaTex, approx 14pagesOperator AlgebrasFunctional Analysis46K05text