On the basis of the classical continuous multi-utility representation theorem of Levin on locally compact and $\sigma$-compact Hausdorff spaces, we present necessary and sufficient conditions on a topological space $(X,t)$ under which every semi-closed and closed preorder respectively admits a continuous multi-utility representation. This discussion provides the fundaments of a mainly topological theory that systematically combines topological and order theoretic aspects of the continuous multi-utility representation problem.
Titolo: | On continuous multi-utility representations of semi-closed and closed preorders |
Autori: | |
Data di pubblicazione: | 2016 |
Rivista: | |
Abstract: | On the basis of the classical continuous multi-utility representation theorem of Levin on locally compact and $\sigma$-compact Hausdorff spaces, we present necessary and sufficient conditions on a topological space $(X,t)$ under which every semi-closed and closed preorder respectively admits a continuous multi-utility representation. This discussion provides the fundaments of a mainly topological theory that systematically combines topological and order theoretic aspects of the continuous multi-utility representation problem. |
Handle: | http://hdl.handle.net/11368/2855977 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.mathsocsci.2015.10.006 |
Appare nelle tipologie: | 1.1 Articolo in Rivista |
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