Topological circle planes and topological quadrangles:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Harlow
Longman [u.a.]
1995
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Pitman research notes in mathematics series
337 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 155 S. graph. Darst. |
| ISBN: | 0582288118 |
Internformat
MARC
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| 100 | 1 | |a Schroth, Andreas Eckhard |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Topological circle planes and topological quadrangles |c Andreas E. Schroth |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow |b Longman [u.a.] |c 1995 | |
| 300 | |a X, 155 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Pitman research notes in mathematics series |v 337 | |
| 502 | |a Vollst. zugl.: Braunschweig, Techn. Univ., Habil.-Schr., 1994 | ||
| 650 | 4 | |a Circle | |
| 650 | 4 | |a Finite generalized quadrangles | |
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Datensatz im Suchindex
| _version_ | 1804125097529704448 |
|---|---|
| adam_text | Contents
Introduction 1
Chapter 1 Circle planes
Introduction 7
1 Definitions and Notation 7
2 Models for classical circle planes 10
3 Derived structures 13
Chapter 2 Antiregular quadrangles
Introduction 16
1 Generalised quadrangles 16
2 Square projections 19
3 The twisting number 22
4 Antiregular quadrangles 27
5 Characterisation of antiregular quadrangles 29
Chapter 3 Laguerre planes and antiregular quadrangles
Introduction 38
1 Laguerre planes constructed from antiregular quadrangles 38
2 Antiregular quadrangles constructed from Laguerre planes 40
3 Constructing topologies on the Lie geometry 43
Chapter 4 Mobius planes and antiregular quadrangles
Introduction 53
1 The Lie geometry of a Mobius plane 54
2 The lifted Lie geometry of a flat Mobius plane 55
3 Constructing topologies on the lifted Lie geometry 58
4 Characterising quadrangles obtained from flat Mobius planes 64
ix
Chapter 5 Minkowski planes and antiregular quadrangles
Introduction 73
1 The point space and parallel classes 74
2 The circle space 74
3 The other spaces 78
4 The derivation of a Minkowski plane 81
5 The Lie geometry of a Minkowski plane 84
6 The lifted Lie geometry of a Minkowski plane 85
7 The topology on the lifted Lie geometry 91
8 Characterising quadrangles obtained from Minkowski planes 99
Chapter 6 Relationships of circle planes
Introduction 113
1 Sisters of Laguerre planes 116
2 Sisters of Mobius planes 117
3 Sisters of Minkowski planes 120
Chapter 7 The problem of Apollonius
Introduction 123
1 The problem of Apollonius in Laguerre planes 129
2 The problem of Apollonius in Mobius planes 132
One point and two circles 134
Three circles 136
3 The problem of Apollonius in Minkowski planes 141
Two points and one circle 141
One point and two circles 141
Three circles 143
Index 149
Glossary 151
References 154
x
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| author | Schroth, Andreas Eckhard |
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| bvnumber | BV010624722 |
| classification_rvk | SI 880 SK 350 SK 380 |
| ctrlnum | (OCoLC)243825029 (DE-599)BVBBV010624722 |
| dewey-full | 516.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.13 |
| dewey-search | 516.13 |
| dewey-sort | 3516.13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Thesis Book |
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| id | DE-604.BV010624722 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:56:09Z |
| institution | BVB |
| isbn | 0582288118 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007086645 |
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| physical | X, 155 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| publisher | Longman [u.a.] |
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| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Schroth, Andreas Eckhard Verfasser aut Topological circle planes and topological quadrangles Andreas E. Schroth 1. publ. Harlow Longman [u.a.] 1995 X, 155 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 337 Vollst. zugl.: Braunschweig, Techn. Univ., Habil.-Schr., 1994 Circle Finite generalized quadrangles Topologie (DE-588)4060425-1 gnd rswk-swf Verallgemeinertes Viereck (DE-588)4187518-7 gnd rswk-swf Kreis (DE-588)4032962-8 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Topologie (DE-588)4060425-1 s DE-604 Verallgemeinertes Viereck (DE-588)4187518-7 s Topologischer Raum (DE-588)4137586-5 s Kreis (DE-588)4032962-8 s Pitman research notes in mathematics series 337 (DE-604)BV000022845 337 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007086645&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schroth, Andreas Eckhard Topological circle planes and topological quadrangles Pitman research notes in mathematics series Circle Finite generalized quadrangles Topologie (DE-588)4060425-1 gnd Verallgemeinertes Viereck (DE-588)4187518-7 gnd Kreis (DE-588)4032962-8 gnd Topologischer Raum (DE-588)4137586-5 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4187518-7 (DE-588)4032962-8 (DE-588)4137586-5 (DE-588)4113937-9 |
| title | Topological circle planes and topological quadrangles |
| title_auth | Topological circle planes and topological quadrangles |
| title_exact_search | Topological circle planes and topological quadrangles |
| title_full | Topological circle planes and topological quadrangles Andreas E. Schroth |
| title_fullStr | Topological circle planes and topological quadrangles Andreas E. Schroth |
| title_full_unstemmed | Topological circle planes and topological quadrangles Andreas E. Schroth |
| title_short | Topological circle planes and topological quadrangles |
| title_sort | topological circle planes and topological quadrangles |
| topic | Circle Finite generalized quadrangles Topologie (DE-588)4060425-1 gnd Verallgemeinertes Viereck (DE-588)4187518-7 gnd Kreis (DE-588)4032962-8 gnd Topologischer Raum (DE-588)4137586-5 gnd |
| topic_facet | Circle Finite generalized quadrangles Topologie Verallgemeinertes Viereck Kreis Topologischer Raum Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007086645&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022845 |
| work_keys_str_mv | AT schrothandreaseckhard topologicalcircleplanesandtopologicalquadrangles |