Foundations of Convex Geometry [Paperback]

This is a self-contained and thorough book on the foundations of Euclidean geometry.This book on the foundations of Euclidean geometry aims to present the subject from the point of view of present day mathematics, taking advantage of all the devlopments since the appearance of Hilberts classic work. The treatment is self-contained and thorough, many results being established under weaker hypotheses than usual.The book can serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.This book on the foundations of Euclidean geometry aims to present the subject from the point of view of present day mathematics, taking advantage of all the devlopments since the appearance of Hilberts classic work. The treatment is self-contained and thorough, many results being established under weaker hypotheses than usual.The book can serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.This book presents the foundations of Euclidean geometry from the point of view of mathematics, taking advantage of all the developments since the appearance of Hilbert's classic work. Here, real affine space is characterized by a small number of axioms involving points and line segments making the treatment self-contained and thorough. This treatment is accessible for final year undergraduates and graduate students, and can also serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.Preface; Introduction; 1. Alignments; 2. Convexity; 3. Linearity; 4. Linearity (continued); 5. Density and unendingness; 6. Desargues; 7. Vector spaces; 8. Completeness; 9. Spaces of convex sets; References; Notations; Axioms; Index.'Altogether al�