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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: https://doi.org/10.1090/memo/0623
MathSciNet review: 1388893
MSC: Primary 20B27; Secondary 06A06, 08A02, 54F50
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. $C$-relations
- 11. Examples of $C$-sets
- 12. The classification of $C$-sets
- 13. A topology for $C$-sets
- 14. Automorphism groups of $C$-sets
- Part IV. General betweenness relations
- 15. $B$-relations and general betweenness relations
- 16. Lines, half-lines and directions in a $B$-set
- 17. The relationship between $B$-sets and semilinear orderings
- 18. Components of $B$-sets
- 19. Branch points and sectors of $B$-sets
- 20. Automorphism groups of $B$-sets
- 21. Improving a $B$-relation to a betweenness relation
- Part V. Abstract direction sets
- 22. $D$-relations
- 23. Examples of $D$-sets
- 24. Structural partitions
- 25. Linking of structural partitions
- 26. The betweenness relation derived from a $D$-relation
- 27. The topology on a $D$-set
- 28. Automorphism groups of $D$-sets
- Part VI. Applications and commentary
- 29. Combinatorial trees and discrete $B$-sets
- 30. Arboreal group theory
- 31. $B$-relations and topological spaces
- 32. Cameron’s tree-like objects
- 33. $B$-relations and partially ordered sets
- 34. Configurations of sets, with applications to permutation groups