betweenness relation
1 Definition
Let be a set. A ternary relation on is said to be a betweenness relation if it has the following properties:
-
O1
if , then ; in other words, the set
is a symmetric relation (http://planetmath.org/Symmetric) for each ; thus, from now on, we may say, without any ambiguity, that is between and if ;
-
O2
if , then ;
-
O3
for each , there is a such that ;
-
O4
for each , there is a such that ;
-
O5
if and , then ;
-
O6
if and , then ;
-
O7
if and , then .
Title | betweenness relation |
---|---|
Canonical name | BetweennessRelation |
Date of creation | 2013-03-22 17:18:44 |
Last modified on | 2013-03-22 17:18:44 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 6 |
Author | Mathprof (13753) |
Entry type | Definition |
Classification | msc 51G05 |
Synonym | axioms of order |
Related topic | SomeTheoremsOnTheAxiomsOfOrder |