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Title: One good title for this book would be: Foundations of Functional Analysis
Review: This book is written in the style Theorem-proof-theorem-proof-...It has hundreds of theorems, hundreds of problems, dozens of lemmas, dozens of examples and remarks.The proofs are informal and easy to follow. The problems are theoretical but are not difficult. Some of them have hints that are true solutions.I enjoyed the chapters about Theory of sets, Linear Operators, Measure, Integration, Differenciability, and the pages about Generalized Functions.I think that the chapters about Topological Spaces and Linear Functions could be more intuitive. Also, the Weak Topology is presented very quickly.
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