ABSTRACT
In this chapter, the authors introduce the notion of a nuclear space and discuss some of the expected and unexpected properties inherent to these spaces. Many aspects of topological vector spaces (especially locally convex ones) can be studied in terms of seminorms. All the spaces the authors deal with tend to be topological vector spaces, so begin with a brief overview of such spaces. Topological vector spaces, in particular locally convex ones, can be viewed as a natural generalization of normed linear spaces. The authors present the basic and relevant results and terminology related to these spaces. Continuing with the theme of separation in a topological vector space the authors have the result which demonstrates that closed sets can be separated from compact sets, provided the sets are disjoint.
