Foundations of convex geometry
著者
書誌事項
Foundations of convex geometry
（Australian Mathematical Society lecture series, 12）
Cambridge University Press, 1998
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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.
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