Foundations of Convex Geometry 0521639700

This book presents the foundations of Euclidean geometry from the point of view of mathematics, taking advantage of all

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Table of contents :
Coppel, W. A.Foundations of convex geometry (Australian MS lecture series,vol.12)(CUP,1998)(ISBN 0521639700)(600dpi)(236p) ......Page 4
Copyright ......Page 5
Contents ......Page 7
AUSTRALIAN MATHEMATICAL SOCIETY LECTURE SERIES ......Page 3
Preface XI ......Page 10
Introduction 1 ......Page 14
1 Partially ordered sets 3 ......Page 16
2 Aligned spaces 6 ......Page 19
3 Anti-exchange alignments 14 ......Page 27
4 Antimatroids 16 ......Page 29
5 Exchange alignments 20 ......Page 33
6 Notes 24 ......Page 37
1 Examples 27 ......Page 40
2 Convex geometries 31 ......Page 44
3 Additional axioms 36 ......Page 49
4 Examples (continued) 43 ......Page 56
5 Notes 47 ......Page 60
1 Lines 49 ......Page 62
2 Linear geometries 54 ......Page 67
3 Helly's theorem and its relatives 66 ......Page 79
1 Faces 71 ......Page 84
2 Polytopes 74 ......Page 87
3 Factor geometries 81 ......Page 94
4 Notes 84 ......Page 97
1 Dense linear geometries 85 ......Page 98
2 Unending linear geometries 95 ......Page 108
3 Cones 103 ......Page 116
4 Polyhedra 109 ......Page 122
5 Notes 114 ......Page 127
1 Introduction 115 ......Page 128
2 Projective geometry 119 ......Page 132
3 The Desargues property 124 ......Page 137
4 Factor geometries 131 ......Page 144
5 Notes 135 ......Page 148
1 Coordinates 137 ......Page 150
2 Isomorphisms 143 ......Page 156
3 Vector sums 150 ......Page 163
4 Notes 154 ......Page 167
1 Introduction 157 ......Page 170
2 Separation properties 164 ......Page 177
3 Fundamental theorem of ordered geometry 172 ......Page 185
4 Metric and norm 178 ......Page 191
5 Notes 182 ......Page 195
1 The Hausdorff metric 185 ......Page 198
2 The space ^(X) 189 ......Page 202
3 Embeddings of %(X) 192 ......Page 205
4 The Krein-Kakutani theorem 196 ......Page 209
5 Notes 209 ......Page 222
References 211 ......Page 224
Notations 216 ......Page 229
Axioms 217 ......Page 230
Index 218 ......Page 231
cover......Page 1

Foundations of Convex Geometry
 0521639700

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