Notes on Topological Vector Spaces

Preface In the notion of a topological vector space, there is a very nice interplay between the algebraic structure of a vector space and a topology on the space, basically so that the vector space operations are continuous mappings. There are also plenty of examples, involving spaces of functions on various domains, perhaps with additional properties, and so on. Here we shall try to give an introduction to these topics, without getting too much into the theory, which is treated more thoroughly in the books in the bibliography. Knowledge of linear algebra is assumed, and some familiarity with elementary topology would be useful, with some of the relevant material being reviewed in the first chapter. ii Contents Preface ii 1 Some background information 1 1.