Handbook of Set-Theoretic Topology

K. Kunen, J. Vaughan

• Publisher: North Holland
• Year: 2014
• Print ISBN:
  9780444865809
• eBook ISBN:
  9781483295152
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest.In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todor?evi? on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.

Table of contents

• Front Cover
• Handbook of Set-Theoretic Topology
• Copyright Page
• Foreword
• Table of Contents
• CHAPTER 1. Cardinal Functions I
• Chapter 2. Cardinal functions II
• Chapter 3. The integers and topology
• Chapter 4. Box products
• Chapter 5. Special subsets of the real line
• Chapter 6. Trees and linearly ordered sets,
• Chapter 7. Basic S and L
• Chapter 8. Martin's Axiom and first-countable S- and L-spaces
• Chapter 9. Covering properties
• Chapter 9. With countably compact or pseudocompact
• Chapter 10. Generalized metric spaces
• Chapter 11. An introduction to βw
• Chapter 12. Countably compact and sequentially compact spaces
• Chapter 13. Initially k-compact and related spaces
• Chapter 14. The theory of nonmetrizable manifolds
• Chapter 15. Normality versus collectionwise normality
• Chapter 16. The normal Moore space conjecture and large cardinals
• Chapter 17. Dowker spaces
• Chapter 18. Products of normal spaces,
• Chapter 19. Versions of Martin's Axiom
• Chapter 20. Random and Cohen reals
• Chapter 21. Applications of the Proper Forcing Axiom
• Chapter 22. Borel measures,
• Chapter 23. Banach spaces and topology
• Chapter 24. Topological groups
• Index