Convenient Vector Spaces of Smooth Functions

By a convenient vector space is meant a locally convex IR-vector space which is separated, bornological and Mackey-complete. The theory of such spaces, initiated in Kr 82], Fr 82], and FGK 83], has evolved into a book FK 88]. In the preliminaries below we outline the principal features of this theory relevant to this paper. We are concerned mainly with questions about the reflexiveness of spaces C^∞(X, ?) for various X and matters closely related to this.