Topologically $Q$-algebras, more

Abstract

Topologically $Q$-algebras, a very convenient generalization of (topological) $Q$-algebras, have been recently considered by {\em A. Najmi} and independently by {\em H. Arizmendi et al.}. Here we extend certain basic results of {\em A. Najmi}. Within the same vein of ideas, we introduce a new class of topological algebras, the {\em ``Cauchy topologically $Q$-algebras"} (Cauchy $tQ$-algebras), that yields a new characterization of the standard advertibly complete algebras, as defined by {\em S. Warner}.