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EnglishLet (X,t) be a topological space. Then a preorder ≾ on (X,t) has a continuous multi-utility representation if there exists a family 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 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.
| Titolo: | Continuous multi-utility representations of preorders |
| Autori: | |
| Data di pubblicazione: | 2012 |
| Rivista: | |
| 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 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 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. |
| Handle: | http://hdl.handle.net/11368/2591622 |
| Digital Object Identifier (DOI): | 10.1016/j.jmateco.2012.05.001 |
| URL: | http://www.sciencedirect.com/science/article/pii/S0304406812000262 |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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