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Algebra in the Stone-Cech Compactification : Theory and Applications.
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 topolog...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
De Gruyter,
2011.
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| Edición: | 2nd ed. |
| Colección: | De Gruyter textbook.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 2.6 Notes3 Ḋ -Ultrafilters and The Stone-Cech Compactification of a Discrete Space; 3.1 Ultrafilters; 3.2 The Topological Space Ḋ; 3.3 Stone-Cech Compactification; 3.4 More Topology of Ḋ; 3.5 Uniform Limits via Ultrafilters; 3.6 The Cardinality of Ḋ; 3.7 Notes; 3.8 Closing Remarks; 4 Ṡ
- The Stone-Cech Compactification of a Discrete Semigroup; 4.1 Extending the Operation to Ṡ; 4.2 Commutativity in Ṡ; 4.3 S *; 4.4 K(Ṡ) and its Closure; 4.5 Notions of Size; 4.6 Notes; 5 Ṡ and Ramsey Theory
- Some Easy Applications; 5.1 Ramsey Theory; 5.2 Idempotents and Finite Products.
- 5.3 Sums and Products in N5.4 Adjacent Finite Unions; 5.5 Compactness; 5.6 Notes; II Algebra of Ṡ; 6 Ideals and Commutativity in Ṡ; 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(Ṡ)p; 6.6 Principal Ideals in Ż; 6.7 Ideals and Density; 6.8 Notes; 7 Groups in Ṡ; 7.1 Zelenyuk's Theorem; 7.2 Semigroups Isomorphic to H; 7.3 Free Semigroups and Free Groups in Ṡ; 7.4 Discrete copies of Z; 7.5 Notes; 8 Cancellation.
- 8.1 Cancellation Involving Elements of S8.2 Right Cancelable Elements in Ṡ; 8.3 Right Cancellation in Ṅ and Ż; 8.4 Left Cancelable Elements in Ṡ; 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 Ṡ; 9.5 Rectangular Semigroups in Ṅ; 9.6 Notes; 10 Homomorphisms; 10.1 Homomorphisms to the Circle Group; 10.2 Homomorphisms from Ṫ into S*; 10.3 Homomorphisms from T* into S*
- 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 Ṡ; 11.4 The Rudin-FrolĐik 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 Ṡ; 13.1 Sums Equal to Products in Ż.