Topologies induced by the representation of a betweenness relation as a family of order relations (Q1738930)
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scientific article; zbMATH DE number 7047510
| Language | Label | Description | Also known as |
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| English | Topologies induced by the representation of a betweenness relation as a family of order relations |
scientific article; zbMATH DE number 7047510 |
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Topologies induced by the representation of a betweenness relation as a family of order relations (English)
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24 April 2019
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The authors represent a betweenness relation as a family of order relations and study the corresponding family of induced (Alexandrov) topologies. The intersection of this family is shown to be the anti-discrete topology. A necessary and sufficient condition is formulated for the supremum of this family of topologies to be the discrete topology. It is stated that the condition holds in the case of a finite set. Furthermore connections between the topology induced by an order relation or a metric and the family of topologies induced by the betweenness relation induced by that order relation or metric are investigated.
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betweenness relation
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topology
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preorder relation
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metric
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