TY  - BOOK
AU  - Adeleke,S.A.
AU  - Neumann,P.M.
TI  - Relations related to betweenness: their structure and automorphisms 
T2  - Memoirs of the American Mathematical Society, 
SN  - 9781470402129 (online)
AV  - QA3QA172 .A57 no. 623
U1  - 510 s511.3/3 21
PY  - 1998///
CY  - Providence, R.I.
PB  - American Mathematical Society
KW  - Ordered algebraic structures
KW  - Betweenness relations (Mathematics)
KW  - Automorphisms
KW  - Permutation groups
N1  - "January 1998, volume 131, number 623 (third of 4 numbers)."; Includes bibliographical references (p. 123-125); 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; Access is restricted to licensed institutions; Electronic reproduction; Providence, Rhode Island; American Mathematical Society; 2012
UR  - http://www.ams.org/memo/0623
UR  - http://dx.doi.org/10.1090/memo/0623
ER  -