Algebra in the Stone-Cech Compactification

Name: Algebra in the Stone-Cech Compactification | Theory and Applications
Brand: De Gruyter
Price: 219.0 EUR
Availability: OnlineOnly

Theory and Applications

Neil Hindman Dona Strauss(Autor*in)

De Gruyter (Verlag)

1. Auflage

Erschienen am 20. April 2011

XIII, 485 Seiten

E-Book

PDF mit Wasserzeichen-DRM

Systemvoraussetzungen

978-3-11-080922-0 (ISBN)

219,00 €inkl. 7% MwSt.

Systemvoraussetzungen

für PDF mit Wasserzeichen-DRM

E-Book Einzellizenz

Als Download verfügbar

Beschreibung

Weitere Details

Weitere Ausgaben

Inhalt

Intro
I. Background Development
Notation
1 Semigroups and Their Ideals
1.1 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
Notes
2 Right Topological Semigroups
2.1 Topological Hierarchy
2.2 Compact Right Topological Semigroups
2.3 Closures and Products of Ideals
2.4 Semitopological Semigroups
2.5 Ellis' Theorem
Notes
3 ßD
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
Notes
Closing Remarks
4 ßS
4.1 Extending the Operation to ßS
4.2 Commutativity in ßS
4.3 S*
4.4 K(ßS) and Its Closure
Notes
5 ßS and Ramsey Theory
5.1 Ramsey Theory
5.2 Idempotents and Finite Products
5.3 Sums and Products in N
5.4 Adjacent Finite Unions
5.5 Compactness
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
6.4 Weakly Left Cancellative Semigroups
6.5 Semiprincipal Left Ideals
6.6 Principal Ideals in ßZ
6.7 Ideals and Density
Notes
7 Groups in ßS
7.1 Zelenuk's Theorem
7.2 Semigroups Isomorphic to H
7.3 Free Semigroups and Free Groups in ßS
Notes
8 Cancellation
8.1 Cancellation Involving Elements of S
8.2 Right Cancelable Elements in ßS
8.3 Right Cancellation in ßN and ßZ
8.4 Left Cancelable Elements in ßS
8.5 Compact Semigroups
Notes
9 Idempotents
9.1 Right Maximal Idempotents
9.2 Topologies Defined by Idempotents
9.3 Chains of Idempotents
9.4 Identities in ßS
Notes
10 Homomorphisms
10.1 Homomorphisms to the Circle Group
10.2 Homomorphisms from ßT into S*
10.3 Homomorphisms from T* into S*
10.4 Isomorphisms on Principal Ideals
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
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
Notes
13 Multiple Structures in ßS
13.1 Sums Equal to Products in ßZ
13.2 The Distributive Laws in ßZ
13.3 Ultrafilters on R Near 0
13.4 Left and Right Continuous Extensions
Notes
III. Combinatorial Applications
14 The Central Sets Theorem
14.1 Van der Waerden's Theorem
14.2 The Hales-Jewett Theorem
14.3 The Commutative Central Sets Theorem
14.4 The Noncommutative Central Sets Theorem
14.5 Combinatorial Characterization
Notes
15 Partition Regularity of Matrices
15.1 Image Partition Regular Matrices
15.2 Kernel Partition Regular Matrices
15.3 Kernel Partition Regularity Over N
15.4 Image Partition Regularity Over N
15.5 Matrices with Entries from Fields
Notes
16 IP, IP*, Central, and Central* Sets
16.1 Sets in Arbitrary Semigroups
16.2 IP* and Central Sets in N
16.3 IP* Sets in Weak Rings
16.4 Spectra and Iterated Spectra
Notes
17 Sums and Products
17.1 Ultrafilters with Rich Structure
17.2 Pairwise Sums and Products
17.3 Sums of Products
17.4 Linear Combinations of Sums
17.5 Sums and Products in (0, 1)
Notes
18 Multidimensional Ramsey Theory
18.1 Ramsey's Theorem and Generalizations
18.2 IP* Sets in Product Spaces
18.3 Spaces of Variable Words
18.4 Carlson's Theorem
Notes
IV. Connections With Other Structures
19 Relations With Topological Dynamics
19.1 Minimal Dynamical Systems
19.2 Enveloping Semigroups
19.3 Dynamically Central Sets
19.4 Dynamically Generated IP* Sets
Notes
20 Density - Connections with Ergodic Theory
20.1 Upper Density and Banach Density
20.2 The Correspondence Principle
20.3 A Density Version of the Finite Sums Theorem
Notes
21 Other Semigroup Compactifications
21.1 The LMC, WAP, AP, and sAP Compactifications
21.2 Right Topological Compactifications
21.3 Periodic Compactifications as Quotients
21.4 Spaces of Filters
21.5 Uniform Compactifications
Notes
Bibliography
List of Symbols
Index

Systemvoraussetzungen

Als PDF speichern Als Link merken