**Contemporary Mathematics**

Volume: 84;
1989;
116 pp;
Softcover

MSC: Primary 03;
Secondary 54

Print ISBN: 978-0-8218-5091-6

Product Code: CONM/84

List Price: $38.00

Individual Member Price: $30.40

**Electronic ISBN: 978-0-8218-7672-5
Product Code: CONM/84.E**

List Price: $38.00

Individual Member Price: $30.40

# Partition Problems in Topology

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*Stevo Todorcevic*

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

# Table of Contents

## Partition Problems in Topology

- Contents ix10 free
- Preface xi12 free
- Introduction 114 free
- 0. The role of countability in (S) and (L) 316
- 1. Oscillating real numbers 1528
- 2. The conjecture (S) for compact spaces 2336
- 3. Some problems closely related to (S) and (L) 2740
- 4. Diagonalizations of length continuum 3548
- 5. (S) and (L) and the Souslin Hypothesis 4558
- 6. (S) and (L) and Luzin spaces 4962
- 7. Forcing axioms for ccc partitions 5770
- 8. Proper forcing axiom and partitions 7184
- 9. (S) and (L) are different 91104
- References 103116
- Index of symbols 113126 free
- Index of terms 115128