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Partition Problems in Topology
 
Front Cover for Partition Problems in Topology
Available Formats:
Softcover ISBN: 978-0-8218-5091-6
Product Code: CONM/84
List Price: $41.00
MAA Member Price: $36.90
AMS Member Price: $32.80
Electronic ISBN: 978-0-8218-7672-5
Product Code: CONM/84.E
List Price: $38.00
MAA Member Price: $34.20
AMS Member Price: $30.40
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Front Cover for Partition Problems in Topology
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Partition Problems in Topology
Available Formats:
Softcover ISBN:  978-0-8218-5091-6
Product Code:  CONM/84
List Price: $41.00
MAA Member Price: $36.90
AMS Member Price: $32.80
Electronic ISBN:  978-0-8218-7672-5
Product Code:  CONM/84.E
List Price: $38.00
MAA Member Price: $34.20
AMS Member Price: $30.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $61.50
MAA Member Price: $55.35
AMS Member Price: $49.20
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 841989; 116 pp
    MSC: Primary 03; Secondary 54;

    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
     
     
    • Chapters
    • Introduction
    • 0. The role of countability in (S) and (L)
    • 1. Oscillating real numbers
    • 2. The conjecture (S) for compact spaces
    • 3. Some problems closely related to (S) and (L)
    • 4. Diagonalizations of length continuum
    • 5. (S) and (L) and the Souslin Hypothesis
    • 6. (S) and (L) and Luzin spaces
    • 7. Forcing axioms for $ccc$ partitions
    • 8. Proper forcing axiom and partitions.
    • 9. (S) and (L) are different
    • References
    • Index of symbols
    • Index of terms
  • Request Review Copy
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Volume: 841989; 116 pp
MSC: Primary 03; Secondary 54;

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.

  • Chapters
  • Introduction
  • 0. The role of countability in (S) and (L)
  • 1. Oscillating real numbers
  • 2. The conjecture (S) for compact spaces
  • 3. Some problems closely related to (S) and (L)
  • 4. Diagonalizations of length continuum
  • 5. (S) and (L) and the Souslin Hypothesis
  • 6. (S) and (L) and Luzin spaces
  • 7. Forcing axioms for $ccc$ partitions
  • 8. Proper forcing axiom and partitions.
  • 9. (S) and (L) are different
  • References
  • Index of symbols
  • Index of terms
Please select which format for which you are requesting permissions.