Relations Related to Betweenness : Their Structure and Automorphisms.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.