Topological groups: characters, dualities, and minimal group topologies
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
1990
|
| Schriftenreihe: | Pure and applied mathematics
130 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 287 S. |
| ISBN: | 0824780477 |
Internformat
MARC
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| 245 | 1 | 0 | |a Topological groups |b characters, dualities, and minimal group topologies |c Dikran N. Dikranjan ; Luchezar N. Stoyanov ; Ivan R. Prodanov |
| 264 | 1 | |a New York [u.a.] |b Dekker |c 1990 | |
| 300 | |a X, 287 S. | ||
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| 490 | 1 | |a Pure and applied mathematics |v 130 | |
| 650 | 4 | |a Topological groups | |
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| 700 | 1 | |a Prodanov, Ivan R. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804117901400080384 |
|---|---|
| adam_text | Contents
PREFACE iii
1. EXISTENCE OF CHARACTERS 1
1.1 Characters of Discrete Abelian Groups 1
1.2 Bogoliouboff Lemma 3
1.3 FfSlner Lemma 7
1.4 F01ner Theorem 12
1.5 Notes 17
1.6 Exercises 24
2. APPLICATIONS OF THE F0LNER THEOREM 30
2.1 Topological Groups: Preliminary Facts 30
2.2 Approximation of Almost Periodic Functions 34
2.3 Precompact Group Topologies on Abelian Groups 35
2.4 Haar Integral in Locally Compact Abelian Groups 38
2.5 Minimal Topologies on Abelian Groups 43
2.6 Localization 46
2.7 Precompactness of Minimal Abelian Groups 48
2.8 Submaximal Topologies on Abelian Groups 55
2.9 Notes 57
2.10 Exercises 64
3. PONTRYAGIN DUALITY 74
3.1 Pontryagin Duality in the Compact Discrete Case 74
3.2 Pontryagin Duality for Locally Compact Abelian Groups 81
3.3 Structure of Locally Compact Abelian Groups 88
3.4 Uniqueness of Pontryagin Duality 96
3.5 The Group of p adic Integers 106
3.6 The Group Q* 113
3.7 Notes 117
3.8 Exercises 120
ix
x Contents
4. QUASI TORSION ELEMENTS IN TOPOLOGICAL GROUPS 127
4.1 Quasi p Torsion Elements 127
4.2 Compact Abelian Groups that Do Not Contain 22^ 134
4.3 Totally Minimal Topological Groups 142
4.4 Notes 148
4.5 Exercises 153
5. MINIMAL ABELIAN GROUPS 162
5.1 Description of Minimal Topologies on Some Abelian Groups 162
5.2 A Characterization of the Groups of p adic Integers 170
5.3 Cardinal Invariants of Minimal Abelian Groups 172
5.4 Notes 176
5.5 Exercises 179
6. MINIMALITY OF PRODUCTS OF TOPOLOGICAL
ABELIAN GROUPS 183
6.1 Finite Products and Perfectly Minimal Groups 183
6.2 Minimality Criterion for Products 194
6.3 Critical Power of Minimality 201
6.4 Notes 207
6.5 Exercises 208
7. MINIMAL AND TOTALLY MINIMAL NONABELIAN GROUPS 214
7.1 Symmetric Topological Groups 214
7.2 Semidirect Products and Their Applications
to Minimal Group Topologies 221
7.3 The Three Space Problem and Products of
(Totally) Minimal Groups 227
7.4 Total Minimality of SL(2,IR) 235
7. 5 Cardinal Invariants of Minimal Groups 241
7.6 Total Minimality of the Unitary Groups 246
7.7 Notes 259
7.8 Exercises 263
NOTATION 269
REFERENCES 273
INDEX 285
|
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| id | DE-604.BV003552067 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:01:46Z |
| institution | BVB |
| isbn | 0824780477 |
| language | English |
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| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Dikranjan, Dikran N. Verfasser aut Topological groups characters, dualities, and minimal group topologies Dikran N. Dikranjan ; Luchezar N. Stoyanov ; Ivan R. Prodanov New York [u.a.] Dekker 1990 X, 287 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 130 Topological groups Topologische Gruppe (DE-588)4135793-0 gnd rswk-swf Minimale topologische Gruppe gnd rswk-swf Topologische Gruppe (DE-588)4135793-0 s DE-604 Minimale topologische Gruppe f Stoyanov, Luchezar N. 1954- Verfasser (DE-588)138018456 aut Prodanov, Ivan R. Verfasser aut Pure and applied mathematics 130 (DE-604)BV000001885 130 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002258675&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dikranjan, Dikran N. Stoyanov, Luchezar N. 1954- Prodanov, Ivan R. Topological groups characters, dualities, and minimal group topologies Pure and applied mathematics Topological groups Topologische Gruppe (DE-588)4135793-0 gnd |
| subject_GND | (DE-588)4135793-0 |
| title | Topological groups characters, dualities, and minimal group topologies |
| title_auth | Topological groups characters, dualities, and minimal group topologies |
| title_exact_search | Topological groups characters, dualities, and minimal group topologies |
| title_full | Topological groups characters, dualities, and minimal group topologies Dikran N. Dikranjan ; Luchezar N. Stoyanov ; Ivan R. Prodanov |
| title_fullStr | Topological groups characters, dualities, and minimal group topologies Dikran N. Dikranjan ; Luchezar N. Stoyanov ; Ivan R. Prodanov |
| title_full_unstemmed | Topological groups characters, dualities, and minimal group topologies Dikran N. Dikranjan ; Luchezar N. Stoyanov ; Ivan R. Prodanov |
| title_short | Topological groups |
| title_sort | topological groups characters dualities and minimal group topologies |
| title_sub | characters, dualities, and minimal group topologies |
| topic | Topological groups Topologische Gruppe (DE-588)4135793-0 gnd |
| topic_facet | Topological groups Topologische Gruppe Minimale topologische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002258675&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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