paper
New characterizations of completely useful topologies in mathematical utility theory
Gianni Bosi, Roberto Daris, Gabriele Sbaiz
New characterizations of completely useful topologies in mathematical utility theory
Gianni Bosi, Roberto Daris, Gabriele Sbaiz
paper2024-02-28English
Description
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.
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