Description
Book SynopsisA Solutions Manual to accompany Geometry of Convex Sets Geometry of Convex Sets begins with basic definitions of the concepts of vector addition and scalar multiplication and then defines the notion of convexity for subsets of n-dimensional space.
Table of ContentsPreface vii
1 Introduction to N-Dimensional Geometry 1
1.2 Points Vectors and Parallel Lines 1
1.2.5 Problems 1
1.4 Inner Product and Orthogonality 3
1.4.3 Problems 3
1.6 Hyperplanes and Linear Functionals 5
1.6.3 Problems 5
2 Topology 13
2.3 Accumulation Points and Closed Sets 13
2.3.4 Problems 13
2.6 Applications of Compactness 20
2.6.5 Problems 20
3 Convexity 35
3.2 Basic Properties of Convex Sets 35
3.2.1 Problems 35
3.3 Convex Hulls 43
3.3.1 Problems 43
3.4 Interior and Closure of Convex Sets 52
3.4.4 Problems 52
3.5 Affine Hulls 55
3.5.4 Problems 55
3.6 Separation Theorems 66
3.6.2 Problems 66
3.7 Extreme Points of Convex Sets 78
3.7.7 Problems 78
4 Helly’s Theorem 89
4.1 Finite Intersection Property 89
4.1.2 Problems 89
4.3 Applications of Helly’s Theorem 92
4.3.9 Problems 92
4.4 Sets of Constant Width 99
4.4.8 Problems 99
Bibliography 109
Index 113
