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Elements of Abstract Analysis

  • Mícheál Ó Searcóid

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Mícheál Ó Searcóid
    Pages 1-40
  3. Mícheál Ó Searcóid
    Pages 41-56
  4. Mícheál Ó Searcóid
    Pages 57-90
  5. Mícheál Ó Searcóid
    Pages 91-114
  6. Mícheál Ó Searcóid
    Pages 115-132
  7. Mícheál Ó Searcóid
    Pages 133-158
  8. Mícheál Ó Searcóid
    Pages 159-176
  9. Mícheál Ó Searcóid
    Pages 177-206
  10. Mícheál Ó Searcóid
    Pages 207-214
  11. Mícheál Ó Searcóid
    Pages 215-230
  12. Mícheál Ó Searcóid
    Pages 231-244
  13. Mícheál Ó Searcóid
    Pages 245-268
  14. Back Matter
    Pages 269-300

About this book

Introduction

In nature's infinite book ofsecrecy A little I can read. Antony and Cleopatra, l. ii. This is a book about a few elementary concepts of analysis and the mathe­ matical structures which enfold them. It is more concerned with the interplay amongst these concepts than with their many applications. The book is self-contained; in the first chapter, after acknowledging the fundamental role ofmathematical logic, wepresent seven axioms of Set Theory; everything else is developed from these axioms. It would therefore be true, if misleading, to say that the reader requires no prior knowledge of mathematics. In reality, the reader we have in mind has that level of sophistication achieved in about three years of undergraduate study of mathematics and is already well acquainted with most of the structures discussed-rings, linear spaces, metric spaces, and soon-and with many ofthe principal analytical concepts­ convergence, connectedness, continuity,compactness and completeness. Indeed, it is only after gaining familiarity with these concepts and their applications that it is possible to appreciate their place within a broad framework of set­ based mathematics and to consolidate an understanding of them in such a framework. To aid in these pursuits, wepresent our reader with things familiar and things new side by side in most parts of the book-and we sometimes adopt an unusual perspective. That this is not an analysis textbook is clear from its many omissions.

Keywords

calculus compactness convergence functional analysis metric space

Authors and affiliations

  • Mícheál Ó Searcóid
    • 1
  1. 1.Department of MathematicsUniversity College DublinBelfieldIreland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-0179-6
  • Copyright Information Springer-Verlag London Limited 2002
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-85233-424-6
  • Online ISBN 978-1-4471-0179-6
  • Series Print ISSN 1615-2085
  • Buy this book on publisher's site
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