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Partition Problems in Topology
Stevo Todorcevic

Contemporary Mathematics
1989; 116 pp; softcover
Volume: 84
Reprint/Revision History:
reprinted 1991
ISBN-10: 0-8218-5091-1
ISBN-13: 978-0-8218-5091-6
List Price: US$38
Member Price: US$30.40
Order Code: CONM/84
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This book presents results on the case of the Ramsey problem for the uncountable: When does a partition of a square of an uncountable set have an uncountable homogeneous set? This problem most frequently appears in areas of general topology, measure theory, and functional analysis. Building on his solution of one of the two most basic partition problems in general topology, the "S-space problem," the author has unified most of the existing results on the subject and made many improvements and simplifications. The first eight sections of the book require basic knowldege of naive set theory at the level of a first year graduate or advanced undergraduate student. The book may also be of interest to the exclusively set-theoretic reader, for it provides an excellent introduction to the subject of forcing axioms of set theory, such as Martin's axiom and the Proper forcing axiom.

Table of Contents

  • The role of countability in (S) and (L)
  • Oscillating real numbers
  • The conjecture (S) for compact spaces
  • Some problems closely related to (S) and (L)
  • Diagonalizations of length continuum
  • (S) and (L) and the Souslin hypothesis
  • (S) and (L) and Luzin spaces
  • Forcing axioms for \(ccc\) partitions
  • Proper forcing axioms and partitions
  • (S) and (L) are different
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