On the structure of completely useful topologies
Keywords:Hereditarily separable topology, Hereditarily Lindelöf-topology, Thin bounded set
AbstractLet 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.
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How to Cite
G. Bosi and G. Herden, “On the structure of completely useful topologies”, Appl. Gen. Topol., vol. 3, no. 2, pp. 145–167, Oct. 2002.
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