linear ordered geometry

An incidence geometry A=(P,n,I) is a linear ordered geometry if there is a strict betweenness relation B defined on the points P0 of A, such that

  • Col1

    (p,q,r)B only if p,q, and r are collinearMathworldPlanetmath (all incidentMathworldPlanetmathPlanetmath with a common line P1);

  • Col2

    for any pairwise distinct collinear points p,q,r, at least one of (p,q,r), (q,r,p), or (r,p,q)B,

We denote the linear ordered geometry by (A,B).

Title linear ordered geometry
Canonical name LinearOrderedGeometry
Date of creation 2013-03-22 17:19:35
Last modified on 2013-03-22 17:19:35
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 4
Author Mathprof (13753)
Entry type Definition
Classification msc 51G05