A Characterization of Ordered Sets and Lattices via Betweenness Relations
Copyright policy )A Characterization of Ordered Sets and Lattices via Betweenness Relations
The authors establish a canonical one-to-one correspondence for a set with at least 3 elements. The one-to-one correspondence is between all betweenness relations satisfying certain axioms and all pairs of inverse ordering ``\(\)'' defined on orderings for which the corresponding Hasse diagram is connected and all maximal chains contain at least 3 elements.
Combinatorics of partially ordered sets, inverse ordering, Partial orders, general, ordered sets, lattices, betweenness relation, Varieties of lattices, Galois correspondences, closure operators (in relation to ordered sets), Structure theory of lattices, Hasse diagram
Combinatorics of partially ordered sets, inverse ordering, Partial orders, general, ordered sets, lattices, betweenness relation, Varieties of lattices, Galois correspondences, closure operators (in relation to ordered sets), Structure theory of lattices, Hasse diagram
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