Foundations of Convex Geometry

Erscheinungsjahr 2007
ISBN: 978-0-521-63970-5
Verlag: Cambridge University Press

Buch, Englisch, Band 12, 236 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 396 g

Reihe: Australian Mathematical Society Lecture Series

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.

Autoren/Hrsg.

Coppel, W. A.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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.