With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn-Banach theorem. 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
Background. Commutative Topological Groups. Completeness. Topological Vector Spaces. Locally Convex Spaces and Seminorms. Bounded Sets. Hahn-Banach Theorems. Duality. Krein-Milman and Banach-Stone Theorems. Vector-Valued Hahn-Banach Theorems. Barreled Spaces. Inductive Limits. Bornological Spaces. Closed Graph Theorems. Reflexivity. Norm Convexities and Approximation. Bibliography. Index.