Continuous multi-utility representations of preorders

Gianni Bosi and Gerhard Herden

Journal of Mathematical Economics, 2012, vol. 48, issue 4, 212-218

Abstract: Let (X,t) be a topological space. Then a preorder ≾ on (X,t) has a continuous multi-utility representation if there exists a family F of continuous and isotonic real-valued functions f on (X,≾,t) such that for all x∈X and all y∈X the inequalities x≾y mean that for all f∈F the inequalities f(x)≤f(y) hold. We discuss the existence of a continuous multi-utility representation by using suitable concepts of continuity of a preorder. In addition, we clarify in detail the relation between the concept of a continuous multi-utility representation and Nachbin’s concept of a normally preordered space.

Keywords: Weakly continuous preorder; Closed preorder; Multi-utility representation (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (18)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:48:y:2012:i:4:p:212-218

DOI: 10.1016/j.jmateco.2012.05.001

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