On the structure of completely useful topologies

Gianni Bosi, Gerhard Herden


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.


Hereditarily separable topology; Hereditarily Lindelöf-topology; Thin bounded set

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1. Preorderable topologies and order-representability of topological spaces
María Jesús Campión, Juan Carlos Candeal, Esteban Induráin
Topology and its Applications  vol: 156  issue: 18  first page: 2971  year: 2009  
doi: 10.1016/j.topol.2009.01.018

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt