strict betweenness relation
1 Definition
A strict betweenness relation is a betweenness relation that satisfies the following axioms:
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for each pair of points and .
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for each such that , there is an such that .
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for each such that , there is an such that .
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if , then .
2 Remarks
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Any strict betweenness relation can be enlarged to a betweenness relation by including all triples of the forms or .
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Conversely, any betweenness relation can be reduced to a strict betweenness relation by removing all triples of the forms just listed. However, it is possible that the “derived” strict betweenness relation is trivial.
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From axiom we have
Title | strict betweenness relation |
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Canonical name | StrictBetweennessRelation |
Date of creation | 2013-03-22 17:18:56 |
Last modified on | 2013-03-22 17:18:56 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 7 |
Author | Mathprof (13753) |
Entry type | Definition |
Classification | msc 51G05 |
Related topic | SomeTheoremsOnStrictBetweennessRelations |