New characterizations of completely useful topologies in mathematical utility theory
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910430988861440 |
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| author | Bosi, Gianni Daris, Roberto Sbaiz, Gabriele |
| author_facet | Bosi, Gianni Daris, Roberto Sbaiz, Gabriele |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18324 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New characterizations of completely useful topologies in mathematical utility theory Bosi, Gianni Daris, Roberto Sbaiz, Gabriele Theoretical Economics General Topology 54F05 (primary), 91B16, 06A05 (secondary) 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. |
| title | New characterizations of completely useful topologies in mathematical utility theory |
| topic | Theoretical Economics General Topology 54F05 (primary), 91B16, 06A05 (secondary) |
| url | https://arxiv.org/abs/2402.18324 |