On the structure of completely useful topologies
[EN] 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 (ZF...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2002 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/82078 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/82078 |
| Access Level: | acceso abierto |
| Palavra-chave: | Hereditarily separable topology Hereditarily Lindelöf-topology Thin bounded set |
| Resumo: | [EN] 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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