Algebra in the Stone-Čech compactification: theory and applications
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin ; New York
<<de>> Gruyter
1998
|
| Series: | De Gruyter expositions in mathematics
27 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 485 S. |
| ISBN: | 311015420X |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
I. Background Development 1
Notation 2
1 Semigroups and Their Ideals 3
1.1 Semigroups 3
1.2 Idempotents and Subgroups 8
1.3 Powers of a Single Element 11
1.4 Ideals 12
1.5 Idempotents and Order 15
1.6 Minimal Left Ideals 19
1.7 Minimal Left Ideals with Idempotents 23
Notes 30
2 Right Topological Semigroups 31
2.1 Topological Hierarchy 31
2.2 Compact Right Topological Semigroups 33
2.3 Closures and Products of Ideals 38
2.4 Semitopological Semigroups 41
2.5 Ellis Theorem 43
Notes 47
3 /SD 48
3.1 Ultrafilters 48
3.2 The Topological Space $D 53
3.3 Stone Cech Compactification 55
3.4 More Topology of $D 58
3.5 Uniform Limits via Ultrafilters 62
3.6 The Cardinality of/3D 66
Notes 69
Closing Remarks 70
4 0S 72
4.1 Extending the Operation to 0 S 72
4.2 Commutativity in 0S 80
ix
x Contents
4.3 S* 82
4.4 K(PS) and Its Closure 85
Notes 88
5 0S and Ramsey Theory 90
5.1 Ramsey Theory 90
5.2 Idempotents and Finite Products 92
5.3 Sums and Products in N 96
5.4 Adjacent Finite Unions 97
5.5 Compactness 101
Notes 102
n. Algebra of pS 105
6 Ideals and Commutativity in pS 107
6.1 The Semigroup M 107
6.2 Intersecting Left Ideals 112
6.3 Numbers of Idempotents and Ideals 114
6.4 Weakly Left Cancellative Semigroups 122
6.5 Semiprincipal Left Ideals 125
6.6 Principal Ideals in pi 131
6.7 Ideals and Density 133
Notes 135
7 Groups in PS 136
7.1 Zelenuk s Theorem 136
7.2 Semigroups Isomorphic to H 148
7.3 Free Semigroups and Free Groups in PS 153
Notes 157
8 Cancellation 158
8.1 Cancellation Involving Elements of 5 158
8.2 Right Cancelable Elements in pS 161
8.3 Right Cancellation in pN and pZ 170
8.4 Left Cancelable Elements in PS 174
8.5 Compact Semigroups 178
Notes 185
9 Idempotents 186
9.1 Right Maximal Idempotents 186
9.2 Topologies Denned by Idempotents 194
9.3 Chains of Idempotents 199
9.4 Identities in PS 202
Notes 204
Contents xi
10 Homomorphisms 205
10.1 Homomorphisms to the Circle Group 206
10.2 Homomorphisms from [5T into S* 210
10.3 Homomorphisms from T* into S* 214
10.4 Isomorphisms on Principal Ideals 218
Notes 221
11 The Rudin Keisler Order 222
11.1 Connections with Right Cancelability 223
11.2 Connections with Left Cancelability in N* 229
11.3 Further Connections with the Algebra of p S 231
11.4 The Rudin Frolik Order 232
Notes 234
12 Ultrafilters Generated by Finite Sums 236
12.1 Martin s Axiom 236
12.2 Strongly Summable Ultrafilters — Existence 240
12.3 Strongly Summable Ultrafilters — Independence 245
12.4 Algebraic Properties 248
Notes 256
13 Multiple Structures in 0 S 258
13.1 Sums Equal to Products in @Z 258
13.2 The Distributive Laws in fil 264
13.3 Ultrafilters on K Near 0 268
13.4 Left and Right Continuous Extensions 272
Notes 275
III. Combinatorial Applications 277
14 The Central Sets Theorem 279
14.1 Van der Waerden s Theorem 279
14.2 The Hales Jewett Theorem 281
14.3 The Commutative Central Sets Theorem 283
14.4 The Noncommutative Central Sets Theorem 286
14.5 Combinatorial Characterization 288
Notes 294
15 Partition Regularity of Matrices 296
15.1 Image Partition Regular Matrices 296
15.2 Kernel Partition Regular Matrices 301
15.3 Kernel Partition Regularity Over N 304
15.4 Image Partition Regularity Over N 308
15.5 Matrices with Entries from Fields 315
Notes 318
xii Contents
16 IP, IP*, Central, and Central* Sets 320
16.1 Sets in Arbitrary Semigroups 320
16.2 IP* and Central Sets in N 324
16.3 IP* Sets in Weak Rings 332
16.4 Spectra and Iterated Spectra 336
Notes 338
17 Sums and Products 339
17.1 Ultrafilters with Rich Structure 339
17.2 Pairwise Sums and Products 341
17.3 Sums of Products 346
17.4 Linear Combinations of Sums 354
17.5 Sums and Products in (0, 1) 361
Notes 367
18 Multidimensional Ramsey Theory 369
18.1 Ramsey s Theorem and Generalizations 369
18.2 IP* Sets in Product Spaces 376
18.3 Spaces of Variable Words 381
18.4 Carlson s Theorem 386
Notes 393
IV. Connections With Other Structures 395
19 Relations With Topological Dynamics 397
19.1 Minimal Dynamical Systems 397
19.2 Enveloping Semigroups 400
19.3 Dynamically Central Sets 404
19.4 Dynamically Generated IP* Sets 407
Notes 411
20 Density — Connections with Ergodic Theory 412
20.1 Upper Density and Banach Density 412
20.2 The Correspondence Principle 417
20.3 A Density Version of the Finite Sums Theorem 419
Notes 424
21 Other Semigroup Compactifications 425
21.1 The £Me,y?A!P, AP, and SA.P Compactifications 425
21.2 Right Topological Compactifications 429
21.3 Periodic Compactifications as Quotients 432
21.4 Spaces of Filters 441
21.5 Uniform Compactifications 445
Notes 453
Contents xiii
Bibliography 455
List of Symbols 471
Index 475
|
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| author | Hindman, Neil 1943- Strauss, Dona 1934- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.32 |
| dewey-search | 514/.32 |
| dewey-sort | 3514 232 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012057483 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:20:54Z |
| institution | BVB |
| isbn | 311015420X |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008160840 |
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| physical | XIII, 485 S. |
| publishDate | 1998 |
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| publisher | <<de>> Gruyter |
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| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Hindman, Neil 1943- Verfasser (DE-588)120427451 aut Algebra in the Stone-Čech compactification theory and applications by Neil Hindman ; Dona Strauss Algebra in the Stone Čech compactification Berlin ; New York <<de>> Gruyter 1998 XIII, 485 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 27 Topologische Halbgruppe - Stone-Čech-Kompaktifizierung Stone-Čech-Kompaktifizierung (DE-588)4308423-0 gnd rswk-swf Topologische Halbgruppe (DE-588)4200462-7 gnd rswk-swf Stone-Čech-Kompaktifizierung (DE-588)4308423-0 s Topologische Halbgruppe (DE-588)4200462-7 s DE-604 Strauss, Dona 1934- Verfasser (DE-588)12042746X aut De Gruyter expositions in mathematics 27 (DE-604)BV004069300 27 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008160840&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hindman, Neil 1943- Strauss, Dona 1934- Algebra in the Stone-Čech compactification theory and applications De Gruyter expositions in mathematics Topologische Halbgruppe - Stone-Čech-Kompaktifizierung Stone-Čech-Kompaktifizierung (DE-588)4308423-0 gnd Topologische Halbgruppe (DE-588)4200462-7 gnd |
| subject_GND | (DE-588)4308423-0 (DE-588)4200462-7 |
| title | Algebra in the Stone-Čech compactification theory and applications |
| title_alt | Algebra in the Stone Čech compactification |
| title_auth | Algebra in the Stone-Čech compactification theory and applications |
| title_exact_search | Algebra in the Stone-Čech compactification theory and applications |
| title_full | Algebra in the Stone-Čech compactification theory and applications by Neil Hindman ; Dona Strauss |
| title_fullStr | Algebra in the Stone-Čech compactification theory and applications by Neil Hindman ; Dona Strauss |
| title_full_unstemmed | Algebra in the Stone-Čech compactification theory and applications by Neil Hindman ; Dona Strauss |
| title_short | Algebra in the Stone-Čech compactification |
| title_sort | algebra in the stone cech compactification theory and applications |
| title_sub | theory and applications |
| topic | Topologische Halbgruppe - Stone-Čech-Kompaktifizierung Stone-Čech-Kompaktifizierung (DE-588)4308423-0 gnd Topologische Halbgruppe (DE-588)4200462-7 gnd |
| topic_facet | Topologische Halbgruppe - Stone-Čech-Kompaktifizierung Stone-Čech-Kompaktifizierung Topologische Halbgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008160840&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004069300 |
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