Bosi, GianniHerden, Gerhard2017-05-312017-05-312002-10-011576-9402https://riunet.upv.es/handle/10251/82078[EN] Let X be an arbitrary set. Then a topology t on X is completely useful if every upper semicontinuous linear preorder on X can be represented by an upper semicontinuous order preserving real-valued function. In this paper we characterize in ZFC (Zermelo-Fraenkel + Axiom of Choice) and ZFC+SH (ZFC + Souslin Hypothesis) completely useful topologies on X. This means, in the terminology of mathematical utility theory, that we clarify the topological structure of any type of semicontinuous utility representation problem.Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)Hereditarily separable topologyHereditarily Lindelöf-topologyThin bounded setArtículo2017-05-3010.4995/agt.2002.2060Abierto1989-4147