Topological Vector Spaces, Second Edition [Hardcover]

With many new concrete examples and historical notes, Topological Vector Spaces, Second Editionprovides one of the most thorough and up-to-date treatments of the HahnBanach theorem. This edition explores the theorems connection with the axiom of choice, discusses the uniqueness of HahnBanach extensions, and includes an entirely new chapter on vector-valued HahnBanach theorems. It also considers different approaches to the BanachStone theorem as well as variations of the theorem.

The book covers locally convex spaces; barreled, bornological, and webbed spaces; and reflexivity. It traces the development of various theorems from their earliest beginnings to present day, providing historical notes to place the results in context. The authors also chronicle the lives of key mathematicians, including Stefan Banach and Eduard Helly.

Suitable for both beginners and experienced researchers, this book contains an abundance of examples, exercises of varying levels of difficulty with many hints, and an extensive bibliography and index.

Background
Topology
Valuation Theory
Algebra
Linear Functionals
Hyperplanes
Measure Theory
Normed Spaces

Commutative Topological Groups
Elementary Considerations
Separation and Compactness
Bases at 0 for Group Topologies
Subgroups and Products
Quotients
S-Topologies
Metrizability

Completeness
Completeness
Function Groups
Total Boundedness
Compactness and Total Boundedness
Uniform Continuity
Extension of Uniformly Continuous Maps
Completion

Topological Vector Spaces
Absorbent and Balanced Sets
ConvexityAlgebraic
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