On a duality with ``less than usual'' reflexive abstract modules

In this paper we study dualities between categories of topological and abstracts modules. Under a ew conditions, any such duality is a restriction of the natural duality between the full subcategories Refl(_R K) and Refl(K_A) of K-reflexive modules, given by the functors Chom_R(-,K) and Hom_A(-,K) for a certain bimodule _RK_A. We are interested to the case where the class Refl(K_A) of reflexive abstract modules is only contained in the class of modules cogenerated by K_A