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.
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