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Upper semicontinuous representations of interval orders

  • Bosi, Gianni
  • Zuanon, Magalì

Given an interval order on a topological space, we characterize its representability by means of a pair of upper semicontinuous real-valued functions. This characterization is only based on separability and continuity conditions related to both the interval order and one of its two traces. As a corollary, we obtain the classical Rader’s theorem concerning the existence of an upper semicontinuous representation for an upper semicontinuous total preorder on a second countable topological space.

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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 68 (2014)
Issue (Month): C ()
Pages: 60-63

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Handle: RePEc:eee:matsoc:v:68:y:2014:i:c:p:60-63
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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  1. Bridges, Douglas S., 1986. "Numerical representation of interval orders on a topological space," Journal of Economic Theory, Elsevier, vol. 38(1), pages 160-166, February.
  2. Alcantud, José Carlos R. & Bosi, Gianni & Zuanon, Magalì, 2009. "A selection of maximal elements under non-transitive indifferences," MPRA Paper 16601, University Library of Munich, Germany.
  3. Alcantud, J. C. R. & Rodriguez-Palmero, C., 1999. "Characterization of the existence of semicontinuous weak utilities," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 503-509, December.
  4. Herden, Gerhard & Levin, Vladimir L., 2012. "Utility representation theorems for Debreu separable preorders," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 148-154.
  5. Subiza, Begona & Peris, Josep E., 1997. "Numerical representation for lower quasi-continuous preferences," Mathematical Social Sciences, Elsevier, vol. 33(2), pages 149-156, April.
  6. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
  7. Chateauneuf, Alain, 1987. "Continuous representation of a preference relation on a connected topological space," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 139-146, April.
  8. Bosi, Gianni & Isler, Romano, 1995. "Representing preferences with nontransitive indifference by a single real-valued function," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 621-631.
  9. Ghanshyam B. Mehta, 1997. "A remark on a utility representation theorem of Rader (*)," Economic Theory, Springer, vol. 9(2), pages 367-370.
  10. J.C. R. Alcantud, 2002. "Characterization of the existence of maximal elements of acyclic relations," Economic Theory, Springer, vol. 19(2), pages 407-416.
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