Handbook of set-theoretic topology

✍ Scribed by Kenneth Kunen; Jerry E Vaughan

• Publisher: North-Holland, , Elsevier B.V
• Year: 1984
• Tongue: English
• Leaves: 1241
• Edition: 1
• Category: Library

✦ Synopsis

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-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martins axiom; and Vaughan and Stephenson on compactness properties.

✦ Table of Contents

Content:
Front Matter, Page iii
Copyright, Page iv
Foreword, Page v, KENNETH KUNEN, JERRY E. VAUGHAN
CHAPTER 1 - Cardinal Functions I, Pages 1,3-61, R. HODEL
CHAPTER 2 - Cardinal Functions II, Pages 63,65-109, I. JUHÁSZ
CHAPTER 3 - The Integers and Topology, Pages 111,113-167, Eric K. VAN DOUWEN
CHAPTER 4 - Box Products, Pages 169,171-200, Scott W. WILLIAMS
CHAPTER 5 - Special Subsets of the Real Line, Pages 201,203-233, Arnold W. MILLER
CHAPTER 6 - Trees and Linearly Ordered Sets, Pages 235,237-293, S. TODORČEVIĆ
CHAPTER 7 - Basic S and L, Pages 295,297-326, Judy ROITMAN
CHAPTER 8 - Martin's Axiom and First-Countable S- and L-Spaces, Pages 327,329-346, U. ABRAHAM, S. TODORČEVIĆ
CHAPTER 9 - Covering Properties, Pages 347,349-422, Dennis K. BURKE
CHAPTER 10 - Generalized Metric Spaces, Pages 423,425-501, Gary GRUENHAGE
CHAPTER 11 - An Introduction to βω, Pages 503,505-567, Jan van MILL
CHAPTER 12 - Countably Compact and Sequentially Compact Spaces, Pages 569,571-602, Jerry E. VAUGHAN
CHAPTER 13 - Initially κ-Compact and Related Spaces, Pages 603,605-632, R.M. STEPHENSON Jr.
CHAPTER 14 - The Theory of Nonmetrizable Manifolds, Pages 633,635-684, Peter NYIKOS
CHAPTER 15 - Normality versus Collectionwise Normality, Pages 685,687-732, Franklin D. TALL
CHAPTER 16 - The Normal Moore Space Conjecture and Large Cardinals, Pages 733,735-760, William G. FLEISSNER
CHAPTER 17 - Dowker Spaces, Pages 761,763-780, Mary Ellen RUDIN
CHAPTER 18 - Products of Normal Spaces, Pages 781,783-826, Teodor C. PRZYMUSIŃSKI
CHAPTER 19 - Versions of Martin's Axiom, Pages 827,829-886, William WEISS
CHAPTER 20 - Random and Cohen Reals, Pages 887,889-911, Kenneth KUNEN
CHAPTER 21 - Applications of the Proper Forcing Axiom, Pages 913,915-959, James E. BAUMGARTNER
CHAPTER 22 - Borel Measures, Pages 961,963-1043, R.J. GARDNER, W.F. PFEFFER
CHAPTER 23 - Banach Spaces and Topology, Pages 1045,1047-1142, S. NEGREPONTIS
CHAPTER 24 - Topological Groups, Pages 1143,1145-1263, W.W. COMFORT
Index, Pages 1265-1273