| Description |
1 online resource (609 pages) |
| Series |
De Gruyter textbook |
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De Gruyter textbook.
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| Contents |
Preface to the First Edition; Preface to the Second Edition; Notation; I Background Development; 1 Semigroups and Their Ideals; 1.1 Semigroups; 1.1.1 Partial Semigroups; 1.2 Idempotents and Subgroups; 1.3 Powers of a Single Element; 1.4 Ideals; 1.5 Idempotents and Order; 1.6 Minimal Left Ideals; 1.7 Minimal Left Ideals with Idempotents; 1.8 Notes; 2 Right Topological (and Semitopological and Topological) Semigroups; 2.1 Topological Hierarchy; 2.2 Compact Right Topological Semigroups; 2.3 Closures and Products of Ideals; 2.4 Semitopological and Topological Semigroups; 2.5 Ellis' Theorem |
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2.6 Notes3 ßD -Ultrafilters and The Stone-Cech Compactification of a Discrete Space; 3.1 Ultrafilters; 3.2 The Topological Space ßD; 3.3 Stone-Cech Compactification; 3.4 More Topology of ßD; 3.5 Uniform Limits via Ultrafilters; 3.6 The Cardinality of ßD; 3.7 Notes; 3.8 Closing Remarks; 4 ßS -- The Stone-Cech Compactification of a Discrete Semigroup; 4.1 Extending the Operation to ßS; 4.2 Commutativity in ßS; 4.3 S *; 4.4 K(ßS) and its Closure; 4.5 Notions of Size; 4.6 Notes; 5 ßS and Ramsey Theory -- Some Easy Applications; 5.1 Ramsey Theory; 5.2 Idempotents and Finite Products |
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5.3 Sums and Products in N5.4 Adjacent Finite Unions; 5.5 Compactness; 5.6 Notes; II Algebra of ßS; 6 Ideals and Commutativity in ßS; 6.1 The Semigroup H; 6.2 Intersecting Left Ideals; 6.3 Numbers of Idempotents and Ideals -- Copies of H; 6.4 Weakly Left Cancellative Semigroups; 6.5 Semiprincipal Left Ideals and the Center of p(ßS)p; 6.6 Principal Ideals in ßZ; 6.7 Ideals and Density; 6.8 Notes; 7 Groups in ßS; 7.1 Zelenyuk's Theorem; 7.2 Semigroups Isomorphic to H; 7.3 Free Semigroups and Free Groups in ßS; 7.4 Discrete copies of Z; 7.5 Notes; 8 Cancellation |
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8.1 Cancellation Involving Elements of S8.2 Right Cancelable Elements in ßS; 8.3 Right Cancellation in ßN and ßZ; 8.4 Left Cancelable Elements in ßS; 8.5 Compact Semigroups Determined by Right Cancelable Elements in Countable Groups; 8.6 Notes; 9 Idempotents; 9.1 Right Maximal Idempotents; 9.2 Topologies Defined by Idempotents; 9.3 Chains of Idempotents; 9.4 Identities in ßS; 9.5 Rectangular Semigroups in ßN; 9.6 Notes; 10 Homomorphisms; 10.1 Homomorphisms to the Circle Group; 10.2 Homomorphisms from ßT into S*; 10.3 Homomorphisms from T* into S* |
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10.4 Isomorphisms Defined on Principal Left and Right Ideals10.5 Notes; 11 The Rudin-Keisler Order; 11.1 Connections with Right Cancelability; 11.2 Connections with Left Cancelability in N*; 11.3 Further Connections with the Algebra of ßS; 11.4 The Rudin-Frolík Order; 11.5 Notes; 12 Ultrafilters Generated by Finite Sums; 12.1 Martin's Axiom; 12.2 Strongly Summable Ultrafilters -- Existence; 12.3 Strongly Summable Ultrafilters -- Independence; 12.4 Algebraic Properties of Strongly Summable Ultrafilters; 12.5 Notes; 13 Multiple Structures in ßS; 13.1 Sums Equal to Products in ßZ |
| Summary |
This book, now in its second revised and extended edition, is a self-contained exposition of the theory of compact right semigroupsfor discrete semigroups and the algebraic properties of these objects. The methods applied in the book constitute a mosaic of infinite combinatorics, algebra and topology. The reader will find numerous combinatorial applications of the theory, including the central sets theorem, partition regularity of matrices, multidimensional Ramsey theory, and many more |
| Notes |
13.2 The Distributive Laws in ßZ |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Stone-Čech compactification.
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Topological semigroups.
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MATHEMATICS -- Topology.
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Stone-Čech compactification
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Topological semigroups
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| Form |
Electronic book
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| Author |
Strauss, Dona
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| ISBN |
9783110258356 |
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3110258358 |
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