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Birkhäuser - Birkhäuser Mathematics | The Structure of the Real Line

The Structure of the Real Line

Series: Monografie Matematyczne, Vol. 71

Bukovský, Lev

2011, XIV, 542 p.

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  • 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
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.

Content Level » Research

Keywords » measure theory - set theory - set topology

Related subjects » Birkhäuser Mathematics

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