In this paper, we provide a characterization of the existence of a representation of an interval order on a topological space in the general case bymeans of a pair of continuous functions, when neither the functions nor the topological space are required to satisfy any particular assumptions. Such a characterization is based on a suitable continuity assumption of the binary relation, called weak continuity. In this way, we generalize all the previous results on the continuous representability of interval orders, and also of total preorders, as particular cases.

Continuous Representations of Interval Orders by Means of Two Continuous Functions

Bosi, Gianni;Estevan, Asier
2020-01-01

Abstract

In this paper, we provide a characterization of the existence of a representation of an interval order on a topological space in the general case bymeans of a pair of continuous functions, when neither the functions nor the topological space are required to satisfy any particular assumptions. Such a characterization is based on a suitable continuity assumption of the binary relation, called weak continuity. In this way, we generalize all the previous results on the continuous representability of interval orders, and also of total preorders, as particular cases.
2020
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https://link.springer.com/article/10.1007/s10957-020-01675-0
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2967523
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