Topological Vector Spaces
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With many new concrete examples and historical notes, this 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 vector-valued Hahn-Banach theorems. It also considers different approaches to the Banach-Stone theorem as well as variations of the theorem. The authors trace the development of various theorems and chronicle the lives of key mathematicians, such as Stefan Banach and Eduar...
With many new concrete examples and historical notes, this 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 vector-valued Hahn-Banach theorems. It also considers different approaches to the Banach-Stone theorem as well as variations of the theorem. The authors trace the development of various theorems and chronicle the lives of key mathematicians, such as Stefan Banach and Eduard Helly.