Abstract. In the framework of the analysis of orderings whose associated indifference relation is not necessarily transitive, we study the structure of an interval order, and its representability through a pair of continuous real-valued functions. Inspired in recent characterizations of the representability of interval orders, we obtain new results concerning the existence of continuous real-valued representations. Classical results are also restated in a unified framework.2000 AMS Classification: 54F05, 06A06.
We present an alternative way to find the general solution of the associativity equation on connected and unlimited totally ordered sets that are representable by utility functions.
This paper is concerned with the representability of totally ordered semigroups as subsets of the additive real line ,ޒ( +, ≤). We prove in an elementary way the existence of an additive utility function.
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