New characterizations of completely useful topologies in mathematical utility theory

Gianni Bosi, Roberto Daris and Gabriele Sbaiz

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Abstract: Let $X$ be an arbitrary set. Then a topology $t$ on $X$ is said to be completely useful if every upper semicontinuous linear (total) preorder $\precsim$ on $X$ can be represented by an upper semicontinuous real-valued order preserving function. In this paper, appealing, simple and new characterizations of completely useful topologies will be proved, therefore clarifying the structure of such topologies.

Date: 2024-02, Revised 2024-05
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