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Partition Problems in Topology

Available Formats:
Softcover ISBN: 978-0-8218-5091-6
Product Code: CONM/84
116 pp
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 116 pp List Price:$38.00
MAA Member Price: $34.20 AMS Member Price:$30.40
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List Price: $61.50 MAA Member Price:$55.35
AMS Member Price: $49.20 Click above image for expanded view Partition Problems in Topology Available Formats:  Softcover ISBN: 978-0-8218-5091-6 Product Code: CONM/84 116 pp  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 116 pp
 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
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
• Request Review Copy
• Get Permissions
Volume: 841989
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
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