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Spaces with non-symmetric distance
About this Title
Eugene M. Zaustinsky
Publication: Memoirs of the American Mathematical Society
Publication Year:
1959; Number 34
ISBNs: 978-0-8218-1234-1 (print); 978-0-8218-9977-9 (online)
DOI: https://doi.org/10.1090/memo/0034
MathSciNet review: 0117686
Table of Contents
Chapters
- Introduction
- Part I. The basic concepts
- 1. General metric spaces
- 2. Compact and finitely compact general metric spaces
- 3. Curves and their lengths. Segments
- 4. Extremals
- 5. Example. The Minkowski geometry
- 6. Example. The quasihyperbolic geometry
- 7. Local homogeneity of $E$-spaces. The one-dimensional $E$-spaces
- Part II. Perpendiculars and parallels
- 8. Convexity of spheres and perpendicularity
- 9. Limitspheres and corays
- 10. Asymptotes and parallels
- Part III. Motions in $E$-spaces
- 11. Axial motions in $E$-spaces
- 12. Translations in straight $E$-surfaces
- 13. Motions of compact $E$-spaces
- Part IV. $E$-spaces with transitive groups of motions
- 14. $E$-spaces with pairwise transitive groups of motions
- 15. The determination of all $E$-surfaces with transitive groups of motions
- Part V. $E$-spaces with non-positive curvature
- 16. Introduction
- 17. Straightness of the universal covering space
- Appendix I. The Funk geometry
- Appendix II. A quasihyperbolic plane