Bosi, GianniEstevan Muguerza, Asier2021-03-102021-04-2120201573-2878 (Electronic)10.1007/s10957-020-01675-0https://academica-e.unavarra.es/handle/2454/39373In 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.20 p.application/pdfeng© Springer Science+Business Media, LLC, part of Springer Nature 2020Interval orderContinuous numerical representationWeak continuityinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessAcceso abierto / Sarbide irekia