Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Prologue: Regular Variation
- 1 Preliminaries
- 2 Baire Category and Related Results
- 3 Borel Sets, Analytic Sets and Beyond: Δ21
- 4 Infinite Combinatorics in Rn: Shift-Compactness
- 5 Kingman Combinatorics and Shift-Compactness
- 6 Groups and Norms: BirkhoffKakutani Theorem
- 7 Density Topology
- 8 Other Fine Topologies
- 9 CategoryMeasure Duality
- 10 Category Embedding Theorem and Infinite Combinatorics
- 11 Effros’ Theorem and the Cornerstone Theorems of Functional Analysis
- 12 Continuity and Coincidence Theorems
- 13 * Non-separable Variants
- 14 Contrasts between Category and Measure
- 15 Interior-Point Theorems: Steinhaus–Weil Theory
- 16 Axiomatics of Set Theory
- Epilogue: Topological Regular Variation
- References
- Index
4 - Infinite Combinatorics in Rn: Shift-Compactness
Published online by Cambridge University Press: 14 January 2025
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Prologue: Regular Variation
- 1 Preliminaries
- 2 Baire Category and Related Results
- 3 Borel Sets, Analytic Sets and Beyond: Δ21
- 4 Infinite Combinatorics in Rn: Shift-Compactness
- 5 Kingman Combinatorics and Shift-Compactness
- 6 Groups and Norms: BirkhoffKakutani Theorem
- 7 Density Topology
- 8 Other Fine Topologies
- 9 CategoryMeasure Duality
- 10 Category Embedding Theorem and Infinite Combinatorics
- 11 Effros’ Theorem and the Cornerstone Theorems of Functional Analysis
- 12 Continuity and Coincidence Theorems
- 13 * Non-separable Variants
- 14 Contrasts between Category and Measure
- 15 Interior-Point Theorems: Steinhaus–Weil Theory
- 16 Axiomatics of Set Theory
- Epilogue: Topological Regular Variation
- References
- Index
Summary
The importance of infinite combinatorics is indicated by the book’s subtitle. Category (and indeed measure) methods are particularly useful for establishing generic behaviour: showing that a particular property predominates, without needing to (or indeed, being able to) show any specific example. Results of this type proved here include the Generic Dichotomy Principle, Generic Completeness Principle, Kestelman–Borwein–Ditor Shift-Compactness Theorem (used many times and abbreviated to KBD) and Kemperman’s Displacement Theorem.
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- Category and MeasureInfinite Combinatorics, Topology and Groups, pp. 71 - 77Publisher: Cambridge University PressPrint publication year: 2025