On a characterization of linear compactness

The aim of the present work is to extend to categories of topological modules the study of the compactness with respect to a closure operator C. We characterize C-compact modules for a regular weakly hereditary closure operator C by properties of the C-separated quotients. In the case when C is the usual Kuratowski closure operator K and the category is that of linearly topologized modules, we obtain a new characterization of the well known class of linearly compact modules as K-compact modules.