Continuous Representations of Interval Orders by Means of Two Continuous Functions

Gianni Bosi and Asier Estevan ()
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Asier Estevan: Universidad Pública de Navarra. Institute INAMAT

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 3, No 2, 700-710

Abstract: 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 by means 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.

Keywords: Interval order; Continuous numerical representation; Weak continuity; 91B06; 91B16 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01675-0

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