Abstract
We find out suitable conditions on a To-principal topology, under which the associated partial order is a partial order with nontransitive incomparability, that is an interval order, a partial semiorder or a semiorder. In order to perform these characterizations, only a T 1 separation axiom is needed. The settheoretical approach allows us to give a simple proof of a fundamental theorem due to Fish burn, concerning the numerical representation of interval orders. We also introduce a class of planar interval orders, called strong interval orders. Although planar posets, as well as interval orders, have arbitrary finite dimension, we prove that a strong interval order is the intersection of at most two linear orders.
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© 1994 Springer Science+Business Media New York
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Isler, R., Bosi, G. (1994). Topological Characterizations of Posets. In: RÃos, S. (eds) Decision Theory and Decision Analysis: Trends and Challenges. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1372-4_10
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DOI: https://doi.org/10.1007/978-94-011-1372-4_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4600-8
Online ISBN: 978-94-011-1372-4
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