Let $X$ be an arbitrary set. Then a topology $t$ on $X$ is said to be \textit{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.
New characterizations of completely useful topologies in mathematical utility theory
Bosi G.;Daris R.;Sbaiz G.
2024-01-01
Abstract
Let $X$ be an arbitrary set. Then a topology $t$ on $X$ is said to be \textit{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.File in questo prodotto:
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