ABSTRACT

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

chapter 1|18 pages

Background

chapter 2|28 pages

Commutative Topological Groups

chapter 3|20 pages

Completeness

chapter 4|48 pages

Topological Vector Spaces

chapter 5|40 pages

Locally Convex Spaces and Seminorms

chapter 6|22 pages

Bounded Sets

chapter 7|48 pages

Hahn–Banach Theorems

chapter 8|50 pages

Duality

chapter 9|66 pages

Krein–Milman and Banach–Stone

chapter 10|30 pages

Vector-Valued Hahn–Banach Theorems

chapter 11|54 pages

Barreled Spaces

chapter 12|16 pages

Inductive Limits

chapter 13|18 pages

Bornological Spaces

chapter 14|26 pages

Closed Graph Theorems

chapter 15|34 pages

Reflexivity

chapter 16|36 pages

Norm Convexities and Approximation