Titlebook: Mathematical Topics on Representations of Ordered Structures and Utility Theory; Essays in Honor of P Gianni Bosi,María J. Campión,Esteban

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Mathematical Topics on Representations of Ordered Structures and Utility Theory978-3-030-34226-5Series ISSN 2198-4182 Series E-ISSN 2198-4190

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Representations of Interval Orders on Connected Separable Topological Spaces generalization of interval representations of interval orders when a continuous strict weak order is given. This allows one to obtain for incomplete preferences one-side or two-sides interval representations and also one-side or two-sides weak interval representations that are partial continuous.

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Searching for a Debreu’s Open Gap Lemma for Semiorderss the problem of finding a utility function was studied until a representability characterization was found. However, there was almost no results on the continuity of the representation. A similar result to Debreu’s Lemma, but for semiorders was never achieved. In the present paper we propose a char

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A Note on Candeal and Induráin’s Semiorder Separability Conditionwith positive threshold can be factorized into two conditions. The first says that the trace of the semiorder must have a numerical representation. The second asserts that the number of “noses” in the semiorder must be finite or countably infinite. We discuss the interest of such a factorization.

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Chain Representations of Nested Families of Biordersg them chain representations, we prove their existence in the finite and countably infinite cases. For the general case, we obtain chain representations in a well-chosen linearly ordered set. Although the existence of real-valued representations in general remains an open problem, our analysis answe

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A Note on Representable Group Topologiess .-topologies. To be precise, groups admitting a non-totally disconnected .-natural topology as well as the non-totally disconnected .-topologies are identified. Moreover, the non-totally disconnected .-representable topologies as well as the total orders inducing non-totally disconnected group top

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