Leseprobe
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Introduction to Ramsey Spaces
Stevo Todorcevic
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Theorem, Characterization (mathematics), Topological group, Baire category theorem, Ideal (ring theory), Topology, Constructible universe, Disjoint sets, Natural number, Forcing (recursion theory), Natural topology, Polish space, Family of sets, Product topology, Subset, Borel measure, Boolean prime ideal theorem, Cantor cube, Cantor set, Dimension (vector space), Infinite product, Dimension, Topological space, Baire space, Compactification (mathematics), Property of Baire, Order type, Schauder basis, Peano axioms, Gap theorem, Monotonic function, Axiom of choice, Subspace topology, Product measure, Right inverse, Cantor space, Borel equivalence relation, Equation, Continuous function (set theory), Limit point, Ramsey's theorem, Semigroup, Mathematical induction, Variable (mathematics), Forcing (mathematics), Open set, Analytic set, Equivalence relation, Lebesgue measure, C0, Set theory, Complete metric space, Continuous function, Corollary, Scalar multiplication, Diagonalization, Borel set, Binary relation, Banach space, Bijection, Lipschitz continuity, Ramsey theory, Sequential space, Metric space, Combinatorics, Probability measure, Metrization theorem, Set (mathematics), Subsequence, Zorn's lemma