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Relations related to betweenness: their structure and automorphisms


About this Title

S. A. Adeleke and Peter M. Neumann

Publication: Memoirs of the American Mathematical Society
Publication Year 1998: Volume 131, Number 623
ISBNs: 978-0-8218-0623-4 (print); 978-1-4704-0212-9 (online)
DOI: http://dx.doi.org/10.1090/memo/0623
MathSciNet review: 1388893
MSC (1991): Primary 20B27; Secondary 06A06, 08A02, 54F50

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Table of Contents


Chapters

  • Part I. Preparation
  • 1. Introduction
  • 2. Terminology and notation
  • 3. Linear relational structures
  • Part II. Semilinear order relations
  • 4. Semilinearly ordered sets
  • 5. Examples of semilinear orderings
  • 6. Automorphism groups of semilinear orderings
  • 7. Maximal chains in semilinear orderings
  • 8. Piecewise linear maximal chains in semilinear orderings
  • 9. Enriching a semilinear ordering
  • Part III. Abstract chain sets
  • 10. -relations
  • 11. Examples of -sets
  • 12. The classification of -sets
  • 13. A topology for -sets
  • 14. Automorphism groups of -sets
  • Part IV. General betweenness relations
  • 15. -relations and general betweenness relations
  • 16. Lines, half-lines and directions in a -set
  • 17. The relationship between -sets and semilinear orderings
  • 18. Components of -sets
  • 19. Branch points and sectors of -sets
  • 20. Automorphism groups of -sets
  • 21. Improving a -relation to a betweenness relation
  • Part V. Abstract direction sets
  • 22. -relations
  • 23. Examples of -sets
  • 24. Structural partitions
  • 25. Linking of structural partitions
  • 26. The betweenness relation derived from a -relation
  • 27. The topology on a -set
  • 28. Automorphism groups of -sets
  • Part VI. Applications and commentary
  • 29. Combinatorial trees and discrete -sets
  • 30. Arboreal group theory
  • 31. -relations and topological spaces
  • 32. Cameron's tree-like objects
  • 33. -relations and partially ordered sets
  • 34. Configurations of sets, with applications to permutation groups