Applications of Point Set Theory in Real Analysis

  • A. B. Kharazishvili

Part of the Mathematics and Its Applications book series (MAIA, volume 429)

Table of contents

  1. Front Matter
    Pages i-viii
  2. A. B. Kharazishvili
    Pages 1-20
  3. A. B. Kharazishvili
    Pages 21-38
  4. A. B. Kharazishvili
    Pages 55-76
  5. A. B. Kharazishvili
    Pages 77-90
  6. A. B. Kharazishvili
    Pages 91-100
  7. A. B. Kharazishvili
    Pages 111-122
  8. A. B. Kharazishvili
    Pages 123-132
  9. A. B. Kharazishvili
    Pages 133-142
  10. A. B. Kharazishvili
    Pages 143-160
  11. A. B. Kharazishvili
    Pages 161-172
  12. A. B. Kharazishvili
    Pages 185-196
  13. A. B. Kharazishvili
    Pages 197-208
  14. A. B. Kharazishvili
    Pages 209-222
  15. Back Matter
    Pages 223-240

About this book

Introduction

This book is devoted to some results from the classical Point Set Theory and their applications to certain problems in mathematical analysis of the real line. Notice that various topics from this theory are presented in several books and surveys. From among the most important works devoted to Point Set Theory, let us first of all mention the excellent book by Oxtoby [83] in which a deep analogy between measure and category is discussed in detail. Further, an interesting general approach to problems concerning measure and category is developed in the well-known monograph by Morgan [79] where a fundamental concept of a category base is introduced and investigated. We also wish to mention that the monograph by Cichon, W«;glorz and the author [19] has recently been published. In that book, certain classes of subsets of the real line are studied and various cardinal­ valued functions (characteristics) closely connected with those classes are investigated. Obviously, the IT-ideal of all Lebesgue measure zero subsets of the real line and the IT-ideal of all first category subsets of the same line are extensively studied in [19], and several relatively new results concerning this topic are presented. Finally, it is reasonable to notice here that some special sets of points, the so-called singular spaces, are considered in the classi

Keywords

measure theory real analysis set set theory topology

Authors and affiliations

  • A. B. Kharazishvili
    • 1
  1. 1.Institute of Applied MathematicsTbilisi State UniversityTbilisiUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-0750-3
  • Copyright Information Springer Science+Business Media B.V. 1998
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5006-9
  • Online ISBN 978-94-017-0750-3
  • About this book
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