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Topological spaces for which every closed and semi-closed preorder respectively admits a continuous multi-utility representation

Bosi, Gianni and Herden, Gerhard (2014): Topological spaces for which every closed and semi-closed preorder respectively admits a continuous multi-utility representation.

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Abstract

On basis of the meanwhile classical continuous multi-utility representation theorem of Levin on locally compact and $\sigma$-compact Hausdorff-spaces the question of characterizing all topological spaces $(X,t)$ for which every closed and semi-closed preorder respectively admits a continuous multi-utility representation will be discussed. In this way we are able to provide the fundaments of a purely topological theory that systematically combines topological and order theoretic aspects of the continuous multi-utility representation problem.

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