Intended as a systematic text on topological vector spaces, this text assumes familiarity with the elements of general topology and linear algebra.

This present first volume begins with the fundamental ideas of general topology. These are of crucial importance for the theory that follows, and so it seems necessary to give a concise account, giving complete proofs.

... Topological. Vector. Spaces. Definition. Let E be a vector space over the field of complex numbers C (in short, a vector space). Let A, ; E X E → E, (x, y) < x + y, M. : C X E → E, (A, x) • Ax, be the vector addition and the scalar ...

... linear map from a topological vector space E into a topological vector space F, f:E/Ker(f) —> F the associated injection (cf. Chapter 1, §4), and <pI E —+ E/Ker( f) the canonical surjection. Since f = f0 p, it follows from the remarks ...

This edition explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes an entirely new chapter on v

This is a softcover reprint of the 1987 English translation of the second edition of Bourbaki's Espaces Vectoriels Topologiques.

Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers.The precise exposition of the first three chapters—covering Banach ...

The lectures associated with these notes were given at the Instituto de Matematica Pura e Aplicada (IMPA) in Rio de Janeiro, during the local winter 1970.