On the structure of completely useful topologies

Gianni Bosi

Italy

Università di Trieste

Department os Applied Mathematics "Bruno de Finetti"

Gerhard Herden

Germany

Universität Essen

Submitted: 2013-12-26

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Accepted: 2013-12-26

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Published: 2002-10-01

DOI: https://doi.org/10.4995/agt.2002.2060
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Keywords:

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

Supporting agencies:

This research was not funded

Abstract:

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.
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