On the structure of completely useful topologies

• Bosi, Gianni ^[1] ; Herden, Gerhard ^[2]
  1. [1] University of Trieste

     University of Trieste

     Trieste, Italia

     
  2. [2] Universität Essen
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 3, Nº. 2, 2002, págs. 145-167
• Idioma: inglés
• DOI: 10.4995/agt.2002.2060
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• Resumen

  • 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.