Document Type

Article

Language

eng

Format of Original

20 p.

Publication Date

12-2013

Publisher

Springer

Source Publication

Bulletin of Mathematical Sciences

Source ISSN

1664-3615

Original Item ID

doi: 10.1007/s13373-013-0040-4

Abstract

A road system is a collection of subsets of a set—the roads—such that every singleton subset is a road in the system and every doubleton subset is contained in a road. The induced ternary (betweenness) relation is defined by saying that a point c lies between points a and b if c is an element of every road that contains both a and b . Traditionally, betweenness relations have arisen from a plethora of other structures on a given set, reflecting intuitions that range from the order-theoretic to the geometric and topological. In this paper we initiate a study of road systems as a simple mechanism by means of which a large majority of the classical interpretations of betweenness are induced in a uniform way.

Comments

Published version. Bulletin of Mathematical Sciences, Vol. 3, No. 3 (December, 2013): 389-408. DOI. © Springer 2013. Used with permission.

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