Introduction to Ramsey Spaces (AM-174)

Přední strana obálky
Princeton University Press, 1. 7. 2010 - Počet stran: 296

Ramsey theory is a fast-growing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. The area of Ramsey theory dealing with Ramsey-type phenomena in higher dimensions is particularly useful. Introduction to Ramsey Spaces presents in a systematic way a method for building higher-dimensional Ramsey spaces from basic one-dimensional principles. It is the first book-length treatment of this area of Ramsey theory, and emphasizes applications for related and surrounding fields of mathematics, such as set theory, combinatorics, real and functional analysis, and topology. In order to facilitate accessibility, the book gives the method in its axiomatic form with examples that cover many important parts of Ramsey theory both finite and infinite.


An exciting new direction for combinatorics, this book will interest graduate students and researchers working in mathematical subdisciplines requiring the mastery and practice of high-dimensional Ramsey theory.

 

Vybrané stránky

Obsah

Introduction
1
Preliminaries
3
Chapter 2 Semigroup Colorings
27
Chapter 3 Trees and Products
49
Chapter 4 Abstract Ramsey Theory
63
Chapter 5 Topological Ramsey Theory
93
Chapter 6 Spaces of Trees
135
Chapter 7 Local Ramsey Theory
179
Chapter 8 Infinite Products of Finite Sets
219
Chapter 9 Parametrized Ramsey Theory
237
Appendix
259
Bibliography
271
Subject Index
279
Index of Notation
285
Autorská práva

Další vydání - Zobrazit všechny

Introduction to Ramsey Spaces
Stevo Todorcevic
Náhled není k dispozici. - 2010
Introduction to Ramsey Spaces
Stevo Todorcevic
Náhled není k dispozici. - 2010

Běžně se vyskytující výrazy a sousloví

analytic Applying assume Baire Class Banach space barrier basic set Borel Cantor space coideal H combinatorial compact constant converging Corollary countable defined Definition denote dense depthy disjoint elements Ellentuck embedding type end-extends equivalence relation fact finishes the proof finite coloring finite sets fusion sequence given H-Ramsey Hales-Jewett theorem Halpern-Läuchli theorem ideal idempotent inductive infinite sequence infinite set infinite subset integer Lebesgue Lebesgue measure Lemma matrix metric metric space minimal Mk+1 monochromatic Nash-Williams Nk+1 nodes nonempty Note notion null open set open subset pair partial semigroup partition perfect set perfect subsets pointwise Polish space positive integer property of Baire Ramsey theorem recursively restriction satisfies semigroup Souslin operation Souslin-measurable coloring strong subtree subsemigroup subspace Suppose theory topological Ramsey space topological space topology tree ultrafilter variable-words Yk+1

O autorovi (2010)

Stevo Todorcevic is professor of mathematics at the University of Toronto and holds senior research positions at the CNRS in Paris and SANU in Belgrade. He is the author or coauthor of several books, including Walks on Ordinals and Their Characteristics and Ramsey Methods in Analysis.

Bibliografické údaje

NázevIntroduction to Ramsey Spaces (AM-174)
Annals of Mathematics Studies – Svazek 174
AutorStevo Todorcevic
Vydáníilustrované vydání
VydavatelPrinceton University Press, 2010
ISBN1400835402, 9781400835409
DélkaPočet stran: 296
  
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