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Continuous multi-utility representations of preorders

  • Bosi, Gianni
  • Herden, Gerhard

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.

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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 48 (2012)
Issue (Month): 4 ()
Pages: 212-218

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Handle: RePEc:eee:mateco:v:48:y:2012:i:4:p:212-218
DOI: 10.1016/j.jmateco.2012.05.001
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