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024 7 $a10.1515/9781400835409
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035   $a(OCoLC)650307489
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035   $a(DE-B1597)9781400835409
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100   $a20090915d2010      uy         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aIntroduction to Ramsey spaces /$fStevo Todorcevic
205   $aCourse Book
210   $aPrinceton $cPrinceton University Press$d2010
215   $a1 online resource (296 p.)
225 1 $aAnnals of mathematics studies ;$v174
300   $aDescription based upon print version of record.
311   $a0-691-14542-3 
311   $a0-691-14541-5 
320   $aIncludes bibliographical references and index.
327   $t Frontmatter -- $tContents -- $tIntroduction -- $tChapter 1. Ramsey Theory: Preliminaries -- $tChapter 2. Semigroup Colorings -- $tChapter 3. Trees and Products -- $tChapter 4. Abstract Ramsey Theory -- $tChapter 5. Topological Ramsey Theory -- $tChapter 6. Spaces of Trees -- $tChapter 7. Local Ramsey Theory -- $tChapter 8. Infinite Products of Finite Sets -- $tChapter 9. Parametrized Ramsey Theory -- $tAppendix -- $tBibliography -- $tSubject Index -- $tIndex of Notation
330   $aRamsey theory is a fast-growing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. The area of Ramsey theory dealing with Ramsey-type phenomena in higher dimensions is particularly useful. Introduction to Ramsey Spaces presents in a systematic way a method for building higher-dimensional Ramsey spaces from basic one-dimensional principles. It is the first book-length treatment of this area of Ramsey theory, and emphasizes applications for related and surrounding fields of mathematics, such as set theory, combinatorics, real and functional analysis, and topology. In order to facilitate accessibility, the book gives the method in its axiomatic form with examples that cover many important parts of Ramsey theory both finite and infinite. An exciting new direction for combinatorics, this book will interest graduate students and researchers working in mathematical subdisciplines requiring the mastery and practice of high-dimensional Ramsey theory.
410  0$aAnnals of mathematics studies ;$v174.
606   $aRamsey theory
606   $aAlgebraic spaces
610   $aAnalytic set.
610   $aAxiom of choice.
610   $aBaire category theorem.
610   $aBaire space.
610   $aBanach space.
610   $aBijection.
610   $aBinary relation.
610   $aBoolean prime ideal theorem.
610   $aBorel equivalence relation.
610   $aBorel measure.
610   $aBorel set.
610   $aC0.
610   $aCantor cube.
610   $aCantor set.
610   $aCantor space.
610   $aCardinality.
610   $aCharacteristic function (probability theory).
610   $aCharacterization (mathematics).
610   $aCombinatorics.
610   $aCompact space.
610   $aCompactification (mathematics).
610   $aComplete metric space.
610   $aCompletely metrizable space.
610   $aConstructible universe.
610   $aContinuous function (set theory).
610   $aContinuous function.
610   $aCorollary.
610   $aCountable set.
610   $aCounterexample.
610   $aDecision problem.
610   $aDense set.
610   $aDiagonalization.
610   $aDimension (vector space).
610   $aDimension.
610   $aDiscrete space.
610   $aDisjoint sets.
610   $aDual space.
610   $aEmbedding.
610   $aEquation.
610   $aEquivalence relation.
610   $aExistential quantification.
610   $aFamily of sets.
610   $aForcing (mathematics).
610   $aForcing (recursion theory).
610   $aGap theorem.
610   $aGeometry.
610   $aIdeal (ring theory).
610   $aInfinite product.
610   $aLebesgue measure.
610   $aLimit point.
610   $aLipschitz continuity.
610   $aMathematical induction.
610   $aMathematical problem.
610   $aMathematics.
610   $aMetric space.
610   $aMetrization theorem.
610   $aMonotonic function.
610   $aNatural number.
610   $aNatural topology.
610   $aNeighbourhood (mathematics).
610   $aNull set.
610   $aOpen set.
610   $aOrder type.
610   $aPartial function.
610   $aPartially ordered set.
610   $aPeano axioms.
610   $aPoint at infinity.
610   $aPointwise.
610   $aPolish space.
610   $aProbability measure.
610   $aProduct measure.
610   $aProduct topology.
610   $aProperty of Baire.
610   $aRamsey theory.
610   $aRamsey's theorem.
610   $aRight inverse.
610   $aScalar multiplication.
610   $aSchauder basis.
610   $aSemigroup.
610   $aSequence.
610   $aSequential space.
610   $aSet (mathematics).
610   $aSet theory.
610   $aSperner family.
610   $aSubsequence.
610   $aSubset.
610   $aSubspace topology.
610   $aSupport function.
610   $aSymmetric difference.
610   $aTheorem.
610   $aTopological dynamics.
610   $aTopological group.
610   $aTopological space.
610   $aTopology.
610   $aTree (data structure).
610   $aUnit interval.
610   $aUnit sphere.
610   $aVariable (mathematics).
610   $aWell-order.
610   $aZorn's lemma.
615  0$aRamsey theory.
615  0$aAlgebraic spaces.
676   $a511/.5
686   $aSI 830$2rvk
700   $aTodorcevic$b Stevo$061532
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910812113303321
996   $aIntroduction to Ramsey spaces$9226789
997   $aUNINA