# On continuous multi-utility representations of semi-closed and closed preorders

*Gianni Bosi* and
*Gerhard Herden*

*Mathematical Social Sciences*, 2016, vol. 79, issue C, 20-29

**Abstract:**
On the basis of the classical continuous multi-utility representation theorem of Levin on locally compact and σ-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.

**Date:** 2016

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:matsoc:v:79:y:2016:i:c:p:20-29

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