On the structure of completely useful topologies

Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)

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2060-6448-1-SM.pdf (327.67 KB)

Fecha

2002-10-01

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https://riunet.upv.es/handle/10251/82078

Cita bibliográfica

Bosi, G.; Herden, G. (2002). On the structure of completely useful topologies. Applied General Topology. 3(2):145-167. https://doi.org/10.4995/agt.2002.2060

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Resumen

[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.

Palabras clave

Hereditarily separable topology, Hereditarily Lindelöf-topology, Thin bounded set

Fuente

Applied General Topology issn: 1576-9402

DOI

10.4995/agt.2002.2060

Versión del editor

https://doi.org/10.4995/agt.2002.2060

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Applied General Topology - Vol 03, No 2 (2002)