The main purpose of this paper
is to indicate a technique for extending certain types of results which are known for
Banach spaces to the corresponding results in more general locally convex topological
vector spaces. We shall extend these results to the class of locally convex spaces
possessing the strict Mackey convergence [SMC] property. The technique involves a
natural embedding into a Banach space and an application of the Banach space
result. Loosely speaking, we have that those properties of closed bounded sets in
Banach spaces that do not depend upon any open set will yield analogous results for
closed bounded sets in quasicomplete locally convex spaces with the SMC
property.
