Foundations of Convex Geometry

This is a self-contained and thorough book on the foundations of Euclidean geometry.

W. A. Coppel (Author)

9780521639705, Cambridge University Press

Paperback, published 5 March 1998

240 pages
22.8 x 15.1 x 1.5 cm, 0.33 kg

'… valuable complement to the large amount of existing literature on 'classical' convexity.' European Mathematical Society

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 developments since the appearance of Hilbert's classic work. Here real affine space is characterised by a small number of axioms involving points and line segments making the treatment self-contained and thorough, many results being established under weaker hypotheses than usual. The treatment should be totally 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.

Subject Areas: Geometry [PBM]