Elements of Abstract Analysis

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Springer, 2002 - Mathematics - 298 pages
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While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis. The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed. It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. The book has been clearly written and contains numerous exercises and examples, making it an a rigorous and self-contained introductory text on functional analysis.
  

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Contents

Linear Structure
115
Geometric Structure
133
Topological Structure
159
Continuity and Openness
177
Connectedness
207
Convergence
215
Compactness
231
Completeness
245
Solutions
269
Bibliography
285
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Elements of Abstract Analysis: Corrigenda
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