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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

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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