2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129183We review our recent formulation of Colombeau type algebras as Hausdorff sequence spaces with ultranorms, defined by sequences of exponential weights. We extend previous results and give new perspectives related to echelon type spaces, possible generalisations, asymptotic algebras, concepts of association, and applications thereof.Functional Analysis46F30; 46A45; 46H05text