Introduction to Ramsey Spaces

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. Introduc...

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Bibliographic Details
Main Author: Todorcevic, Stevo
Format: eBook Book
Language:English
Published: Princeton Princeton University Press 2010
Edition:1
Series:Annals of mathematics studies
Subjects:
Algebraic spaces
Analytic set
Axiom of choice
Baire category theorem
Baire space
Banach space
Bijection
Binary relation
Boolean prime ideal theorem
Borel equivalence relation
Borel measure
Borel set
Cantor cube
Cantor set
Cantor space
Characterization (mathematics)
Combinatorics
Compactification (mathematics)
Complete metric space
Constructible universe
Continuous function
Continuous function (set theory)
Corollary
Diagonalization
Dimension
Dimension (vector space)
Disjoint sets
Equation
Equivalence relation
Family of sets
Forcing (mathematics)
Forcing (recursion theory)
Gap theorem
Ideal (ring theory)
Infinite product
Lebesgue measure
Limit point
Lipschitz continuity
Mathematical induction
MATHEMATICS
MATHEMATICS / Combinatorics
MATHEMATICS / General
Metric space
Metrization theorem
Monotonic function
Natural number
Natural topology
Open set
Order type
Peano axioms
Polish space
Probability measure
Product measure
Product topology
Property of Baire
Ramsey theory
Ramsey's theorem
Right inverse
Scalar multiplication
Schauder basis
Semigroup
Sequential space
Set (mathematics)
Set theory
Subsequence
Subset
Subspace topology
Theorem
Topological group
Topological space
Topology
Variable (mathematics)
Zorn's lemma
Equivalence relation
Open set
Bijection
Subset
Forcing (recursion theory)
Limit point
Product measure
Ramsey theory
Forcing (mathematics)
Cantor set
Borel equivalence relation
Mathematical induction
Characterization (mathematics)
Infinite product
Order type
Combinatorics
Corollary
Monotonic function
Ideal (ring theory)
Right inverse
Baire category theorem
Semigroup
Continuous function
Natural topology
Topology
Sequential space
Subspace topology
Binary relation
Dimension (vector space)
Zorn's lemma
Topological space
Gap theorem
Subsequence
Boolean prime ideal theorem
Disjoint sets
Axiom of choice
Probability measure
Natural number
Complete metric space
Continuous function (set theory)
Diagonalization
Metric space
Product topology
Ramsey's theorem
Set (mathematics)
C0
Cantor space
Lipschitz continuity
Family of sets
Lebesgue measure
Baire space
Theorem
Polish space
Metrization theorem
Borel measure
Peano axioms
Constructible universe
Cantor cube
Borel set
Equation
Dimension
Banach space
Analytic set
Property of Baire
Variable (mathematics)
Topological group
Compactification (mathematics)
Set theory
Schauder basis
Scalar multiplication
ISBN:0691145415, 9780691145419, 9780691145426, 0691145423, 1400835402, 9781400835409
Online Access:Get full text
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Description
Summary: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.
Bibliography:Includes bibliographical references (p. [271]-278) and indexes
ISBN:0691145415
9780691145419
9780691145426
0691145423
1400835402
9781400835409
DOI:10.1515/9781400835409