Cover
Half Title
Title Page
Copyright Page
Contents
Preface
CHAPTER 1: The index of an isometric embedding
CHAPTER 2: Maximal ot-subsets of the Euclidean plane
CHAPTER 3: The cardinalities of at-sets in a real Hilbert space
CHAPTER 4: Isosceles triangles and it-sets in Euclidean space
CHAPTER 5: Some geometric consequences of Ramseyโs combinatorial theorem
CHAPTER 6: Convexly independent subsets of infinite sets of points
CHAPTER 7: Homogeneous coverings of the Euclidean plane
CHAPTER 8: Three-colorings of the Euclidean plane and associated triangles of a prescribed type
CHAPTER 9: Chromatic numbers of graphs associated with point sets in Euclidean space
CHAPTER 10: The SzemerรฉdiโTrotter theorem and its applications
CHAPTER 11: Minkowskiโs theorem, number theory, and nonmeasurable sets
CHAPTER 12: Tarskiโs plank problem
CHAPTER 13: Borsukโs conjecture
CHAPTER 14: Piecewise affine approximations of continuous functions of several variables and CaratheodoryโGale polyhedra
CHAPTER 15: Dissecting a square into triangles of equal areas
CHAPTER 16: Geometric realizations of finite and infinite families of sets
CHAPTER 17: A geometric form of the Axiom of Choice
APPENDIX 1: Convex sets in real vector spaces
APPENDIX 2: Real-valued convex functions
APPENDIX 3: The Principle of Inclusion and Exclusion
APPENDIX 4: The ErdรถsโMordell inequality
APPENDIX 5: Some facts from graph theory
BIBLIOGRAPHY
INDEX