Classification and orbit equivalence relations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2000
|
| Series: | Mathematical surveys and monographs
75 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 189 - 191 |
| Physical Description: | XVII, 195 S. graph. Darst. |
| ISBN: | 0821820028 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface xj
Chapter 1. An outline 1
1.1. Some specific classification problems 1
1.2. The form of this book (and one time paper) 2
1.3. Acknowledgments 3
Chapter 2. Definitions and technicalities 5
2.1. Polish groups and Polish spaces 5
2.2. Equivalence relations 15
2.3. Spaces of countable structures 18
2.4. Baire category methods 23
Chapter 3. Turbulence 37
3.1. Generic ergodicity 37
3.2. The definition of turbulence 41
3.3. Examples 52
3.4. Historical remarks 55
Chapter 4. Classifying homeomorphisms 59
4.1. Definitions and remarks 59
4.2. Classification in dimension 1 61
4.3. Non classification in dimension 2 66
4.4. Remarks and connections 74
Chapter 5. Infinite dimensional group representations 75
Chapter 6. A generalized Scott analysis 81
6.1. A preliminary discussion of a specific case 81
6.2. The general case 93
6.3. A counterexample 108
6.4. A different direction 111
Chapter 7. GE groups 115
7.1. More on Polish groups; Glimm Effros: Gg orbits 115
7.2. Invariantly metrizable and nilpotent are GE 128
7.3. Dynamic changes in topologies 134
7.4. Products of locally compact groups 139
7.5. CLI groups have the weak Glimm Effros property 145
Chapter 8. The dark side 149
ix
x CONTENTS
Chapter 9. Beyond Borel 155
9.1. Two theorems by transfinite changes in topologies 155
9.2. Cardinality in L(M) 169
Chapter 10. Looking ahead 177
Appendix A. Ordinals 181
Appendix B. Notation 185
Bibliography 189
Index 193
|
| adam_txt |
Contents
Preface xj
Chapter 1. An outline 1
1.1. Some specific classification problems 1
1.2. The form of this book (and one time paper) 2
1.3. Acknowledgments 3
Chapter 2. Definitions and technicalities 5
2.1. Polish groups and Polish spaces 5
2.2. Equivalence relations 15
2.3. Spaces of countable structures 18
2.4. Baire category methods 23
Chapter 3. Turbulence 37
3.1. Generic ergodicity 37
3.2. The definition of turbulence 41
3.3. Examples 52
3.4. Historical remarks 55
Chapter 4. Classifying homeomorphisms 59
4.1. Definitions and remarks 59
4.2. Classification in dimension 1 61
4.3. Non classification in dimension 2 66
4.4. Remarks and connections 74
Chapter 5. Infinite dimensional group representations 75
Chapter 6. A generalized Scott analysis 81
6.1. A preliminary discussion of a specific case 81
6.2. The general case 93
6.3. A counterexample 108
6.4. A different direction 111
Chapter 7. GE groups 115
7.1. More on Polish groups; Glimm Effros: Gg orbits 115
7.2. Invariantly metrizable and nilpotent are GE 128
7.3. Dynamic changes in topologies 134
7.4. Products of locally compact groups 139
7.5. CLI groups have the weak Glimm Effros property 145
Chapter 8. The dark side 149
ix
x CONTENTS
Chapter 9. Beyond Borel 155
9.1. Two theorems by transfinite changes in topologies 155
9.2. Cardinality in L(M) 169
Chapter 10. Looking ahead 177
Appendix A. Ordinals 181
Appendix B. Notation 185
Bibliography 189
Index 193 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T16:18:14Z |
| indexdate | 2024-07-09T20:51:26Z |
| institution | BVB |
| isbn | 0821820028 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015366360 |
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| physical | XVII, 195 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Hjorth, Greg Verfasser aut Classification and orbit equivalence relations Greg Hjorth Providence, RI American Math. Soc. 2000 XVII, 195 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 75 Literaturverz. S. 189 - 191 Classes d'équivalence (Théorie des ensembles) Classes d'équivalence (Théorie des ensembles) ram Classification Classification ram Lógica matemática larpcal Relations d'équivalence (Théorie des ensembles) Relations d'équivalence (Théorie des ensembles) ram Teoria dos conjuntos (textos avançados) larpcal Equivalence classes (Set theory) Equivalence relations (Set theory) Orbit Mathematik (DE-588)4238277-4 gnd rswk-swf Äquivalenzrelation (DE-588)4141500-0 gnd rswk-swf Klassifikationstheorie (DE-588)4164034-2 gnd rswk-swf Äquivalenzrelation (DE-588)4141500-0 s DE-604 Klassifikationstheorie (DE-588)4164034-2 s Orbit Mathematik (DE-588)4238277-4 s Erscheint auch als Online-Ausgabe 978-1-4704-1302-6 Mathematical surveys and monographs 75 (DE-604)BV000018014 75 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015366360&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hjorth, Greg Classification and orbit equivalence relations Mathematical surveys and monographs Classes d'équivalence (Théorie des ensembles) Classes d'équivalence (Théorie des ensembles) ram Classification Classification ram Lógica matemática larpcal Relations d'équivalence (Théorie des ensembles) Relations d'équivalence (Théorie des ensembles) ram Teoria dos conjuntos (textos avançados) larpcal Equivalence classes (Set theory) Equivalence relations (Set theory) Orbit Mathematik (DE-588)4238277-4 gnd Äquivalenzrelation (DE-588)4141500-0 gnd Klassifikationstheorie (DE-588)4164034-2 gnd |
| subject_GND | (DE-588)4238277-4 (DE-588)4141500-0 (DE-588)4164034-2 |
| title | Classification and orbit equivalence relations |
| title_auth | Classification and orbit equivalence relations |
| title_exact_search | Classification and orbit equivalence relations |
| title_exact_search_txtP | Classification and orbit equivalence relations |
| title_full | Classification and orbit equivalence relations Greg Hjorth |
| title_fullStr | Classification and orbit equivalence relations Greg Hjorth |
| title_full_unstemmed | Classification and orbit equivalence relations Greg Hjorth |
| title_short | Classification and orbit equivalence relations |
| title_sort | classification and orbit equivalence relations |
| topic | Classes d'équivalence (Théorie des ensembles) Classes d'équivalence (Théorie des ensembles) ram Classification Classification ram Lógica matemática larpcal Relations d'équivalence (Théorie des ensembles) Relations d'équivalence (Théorie des ensembles) ram Teoria dos conjuntos (textos avançados) larpcal Equivalence classes (Set theory) Equivalence relations (Set theory) Orbit Mathematik (DE-588)4238277-4 gnd Äquivalenzrelation (DE-588)4141500-0 gnd Klassifikationstheorie (DE-588)4164034-2 gnd |
| topic_facet | Classes d'équivalence (Théorie des ensembles) Classification Lógica matemática Relations d'équivalence (Théorie des ensembles) Teoria dos conjuntos (textos avançados) Equivalence classes (Set theory) Equivalence relations (Set theory) Orbit Mathematik Äquivalenzrelation Klassifikationstheorie |
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