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arXiv · 2401.13392

A topological study for the existence of lower-semicontinuous Richter-Peleg multi-utilities

Gianni Bosi·Asier Estevan·Armajac Raventós
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Abstract

In the present paper we study necessary and sufficient conditions for the existence of a semicontinuous and finite Richter-Peleg multi-utility for a preorder. It is well know that, given a preorder on a topological space, if there is a lower (upper) semicontinuous Richter-Peleg multi-utility, then the topology of the space must be finer than the Upper (resp. Lower) topology. However, this condition does not guarantee the existence of a semicontinuous representation. We search for finer topologies which are necessary for semicontinuity, as well as that they could guarantee the existence of a semicontinuous representation. As a result, we prove that Scott topology (that refines the Upper one) must be contained in the topology of the space in case there exists a finite lower semicontinuous Richter-Peleg multi-utility. However, as it is shown, the existence of this representation cannot be guaranteed.

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Gianni Bosi, Asier Estevan, Armajac Raventós. 2024-01-24. A topological study for the existence of lower-semicontinuous Richter-Peleg multi-utilities. https://doi.org/10.1007/s11238-019-09730-7

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