The Structure of the Real Line

  • Lev Bukovský

Part of the Monografie Matematyczne book series (MONOGRAFIE, volume 71)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Lev Bukovský
    Pages 1-38
  3. Lev Bukovský
    Pages 39-71
  4. Lev Bukovský
    Pages 73-125
  5. Lev Bukovský
    Pages 127-159
  6. Lev Bukovský
    Pages 161-214
  7. Lev Bukovský
    Pages 215-248
  8. Lev Bukovský
    Pages 249-291
  9. Lev Bukovský
    Pages 293-371
  10. Lev Bukovský
    Pages 373-414
  11. Lev Bukovský
    Pages 415-454
  12. Lev Bukovský
    Pages 455-491
  13. Back Matter
    Pages 493-536

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.


measure theory set theory set topology

Authors and affiliations

  • Lev Bukovský
    • 1
  1. 1., Institute of MathematicsUniversity of P.J. ŠafárikKošiceSlovakia

Bibliographic information