Monografie Matematyczne

The Structure of the Real Line

Authors: Bukovský, Lev

  • Study of the real line taking into account recent results of set theory
  • Self-contained, all necessary results being revisited
  • Includes appendix with concise explanation of the metamathematics behind set theory
  • Exercises with additional results at the end of each section
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  • ISBN 978-3-0348-0006-8
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Hardcover $149.00
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  • ISBN 978-3-0348-0005-1
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  • ISBN 978-3-0348-0321-2
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About this book

The rapid development of set theory in the last fifty years, mainly in obtaining plenty of independence results, strongly influenced an understanding of the structure of the real line. This book is devoted to the study of the real line and its subsets taking into account the recent results of set theory. Whenever possible the presentation is done without the full axiom of choice. Since the book is intended to be self-contained, all necessary results of set theory, topology, measure theory, descriptive set theory are revisited with the purpose to eliminate superfluous use of an axiom of choice. The duality of measure and category is studied in a detailed manner. Several statements pertaining to properties of the real line are shown to be undecidable in set theory. The metamathematics behind it is shortly explained in the appendix. Each section contains a series of exercises with additional results.

Reviews

From the reviews:

“The history of investigations of real numbers is the starting point of this monograph. … Every chapter is supplied with a well-chosen series of exercises containing interesting complementary material. … This unique monograph presents beautiful scientific work prepared in a professional style and built upon a number of references to prominent mathematicians living in previous epochs … . A wide variety of researchers and students will find in it a large … attractive body of knowledge that should be highly inspiring in their work.” (Marek Balcerzak, Mathematical Reviews, Issue 2012 d)

“The book under review is addressed to experts and begins to address some of the questions about the complexities of the real line. … The author provides an appendix with background material on set theory, algebra, topology and metamathematics.” (William J. Satzer, The Mathematical Association of America, August, 2011)


Table of contents (11 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-0006-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-0348-0005-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-0348-0321-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Structure of the Real Line
Authors
Series Title
Monografie Matematyczne
Series Volume
71
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Spinger Basel AG
eBook ISBN
978-3-0348-0006-8
DOI
10.1007/978-3-0348-0006-8
Hardcover ISBN
978-3-0348-0005-1
Softcover ISBN
978-3-0348-0321-2
Series ISSN
0077-0507
Edition Number
1
Number of Pages
XIV, 542
Topics