Foundations of convex geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
1998
|
| Ausgabe: | 1 publ. |
| Schriftenreihe: | Australian Mathematical Society lecture series
12 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 222 S. |
| ISBN: | 0521639700 |
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| 245 | 1 | 0 | |a Foundations of convex geometry |c W. A. Coppel |
| 250 | |a 1 publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 1998 | |
| 300 | |a XIV, 222 S. | ||
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| 490 | 1 | |a Australian Mathematical Society lecture series |v 12 | |
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Datensatz im Suchindex
| _version_ | 1804142005035466752 |
|---|---|
| adam_text | Contents
Preface xi
Introduction 1
I Alignments 3
1 Partially ordered sets 3
2 Aligned spaces 6
3 Anti-exchange alignments 14
4 Antimatroids 16
5 Exchange alignments 20
6 Notes 24
II Convexity 27
1 Examples 27
2 Convex geometries 31
3 Additional axioms 36
4 Examples (continued) 43
5 Notes 47
III Linearity 49
1 Lines 49
2 Linear geometries 54
3 Helly s theorem and its relatives 66
VIII Contents
IV Linearity (continued) 71
1 Faces 71
2 Polytopes 74
3 Factor geometries 81
4 Notes 84
V Density and Unendingness 85
1 Dense linear geometries 85
2 Unending linear geometries 95
3 Cones 103
4 Polyhedra 109
5 Notes 114
VI Desargues 115
1 Introduction 115
2 Projective geometry 119
3 The Desargues property 124
4 Factor geometries 131
5 Notes 135
VII Vector Spaces 137
1 Coordinates 137
2 Isomorphisms 143
3 Vector sums 150
4 Notes 154
VIII Completeness 157
1 Introduction 157
2 Separation properties 164
3 Fundamental theorem of ordered geometry 172
4 Metric and norm 178
5 Notes 182
Contents DC
IX Spaces of Convex Sets 185
1 The Hausdorff metric 185
2 The space €(X) 189
3 Embeddings of €(X) 192
4 The Krein-Kakutani theorem 196
5 Notes 209
References 211
Notations 216
Axioms 217
Index 218
|
| any_adam_object | 1 |
| author | Coppel, William A. |
| author_GND | (DE-588)108974839 |
| author_facet | Coppel, William A. |
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| dewey-full | 516.08 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.08 |
| dewey-search | 516.08 |
| dewey-sort | 3516.08 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1 publ. |
| format | Book |
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| indexdate | 2024-07-09T22:24:53Z |
| institution | BVB |
| isbn | 0521639700 |
| language | English |
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| physical | XIV, 222 S. |
| publishDate | 1998 |
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| publisher | Cambridge Univ. Press |
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| series | Australian Mathematical Society lecture series |
| series2 | Australian Mathematical Society lecture series |
| spelling | Coppel, William A. Verfasser (DE-588)108974839 aut Foundations of convex geometry W. A. Coppel 1 publ. Cambridge Cambridge Univ. Press 1998 XIV, 222 S. txt rdacontent n rdamedia nc rdacarrier Australian Mathematical Society lecture series 12 Australian Mathematical Society lecture series 12 (DE-604)BV001902595 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019642863&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Coppel, William A. Foundations of convex geometry Australian Mathematical Society lecture series |
| title | Foundations of convex geometry |
| title_auth | Foundations of convex geometry |
| title_exact_search | Foundations of convex geometry |
| title_full | Foundations of convex geometry W. A. Coppel |
| title_fullStr | Foundations of convex geometry W. A. Coppel |
| title_full_unstemmed | Foundations of convex geometry W. A. Coppel |
| title_short | Foundations of convex geometry |
| title_sort | foundations of convex geometry |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019642863&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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