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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Hlavní autor:	Todorcevic, Stevo
Médium:	E-kniha Kniha
Jazyk:	angličtina
Vydáno:	Princeton Princeton University Press 2010
Vydání:	1
Edice:	Annals of mathematics studies
Témata:	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
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Popis
Shrnutí:	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.
Bibliografie:	Includes bibliographical references (p. [271]-278) and indexes
ISBN:	0691145415 9780691145419 9780691145426 0691145423 1400835402 9781400835409
DOI:	10.1515/9781400835409