ABSTRACT
Many questions in functional analysis lead to a consideration of inductive limits of Frechet or even Banach spaces. This chapter utilizes many facts and ideas from the theory of bases, nuclear spaces and the general theory of locally convex spaces. It considers F to be the dual of a nuclear Frechet space E. F will be equipped with the strong topology. The chapter also utilizes a method which consists of first embedding E' in a space which has a basis, and then constructing a certain block basic sequence which can be approximated by a sequence in E', and an old perturbation theorem of L.
