TY  - BOOK
AU  - Adeleke,S.A.
AU  - Neumann,Peter M.
TI  - Relations Related to Betweenness: Their Structure and Automorphisms
T2  - Memoirs of the American Mathematical Society
SN  - 9781470402129
AV  - QA172 -- .A34 1998eb 
U1  - 510 s;511.3/3 
PY  - 1998///
CY  - Providence
PB  - American Mathematical Society
KW  - Ordered algebraic structures
KW  - Betweenness relations (Mathematics)
KW  - Automorphisms
KW  - Permutation groups
KW  - Electronic books
N1  - Intro -- CONTENTS -- 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 -- REFERENCES
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114419
ER  -