Bibliothèque de L'IMIST/CNRST

"Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines"--Provided by publisher.

"LOCALLY CONVEX SPACES OVER NON-ARCHIMEDEAN VALUED FIELDS Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines. CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS"--Provided by publisher.

Includes bibliographical references and index.

Ultrametrics and valuations -- Normed spaces -- Locally convex spaces -- The Hahn-Banach theorem -- The weak topology -- C-compactness -- Barrelledness and reflexivity -- Montel and nuclear spaces -- Spaces with an "orthogonal" base -- Tensor products -- Inductive limits.