The aim of this paper is to describe some “topological” subclasses of the class of all semi-topological functors. This is done by considering intersections of certain classes: on the one hand, the classes of all semi-topological functors, all topologically-algebraic functors and all regular functors; and on the other hand, the class of all discrete functors (see [6]). The relations between these and other classes of functors are given along with the necessary examples. Finally, the resulting intersections are described by giving representations of the functors that belong to them.