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On the continuous analogue of the Szpilrajn Theorem I

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  • Herden, Gerhard
  • Pallack, Andreas

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  • Herden, Gerhard & Pallack, Andreas, 2002. "On the continuous analogue of the Szpilrajn Theorem I," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 115-134, March.
    • Handle: RePEc:eee:matsoc:v:43:y:2002:i:2:p:115-134
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    1. Herden, G., 1989. "On the existence of utility functions," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 297-313, June.
    2. Klaus Nehring & Clemens Puppe, 1998. "Extended partial orders:A unifying structure for abstract choice theory," Annals of Operations Research, Springer, vol. 80(0), pages 27-48, January.
    3. Herden, G., 1989. "On the existence of utility functions ii," Mathematical Social Sciences, Elsevier, vol. 18(2), pages 107-117, October.
    4. Mehta, Ghanshyam, 1988. "Some general theorems on the existence of order-preserving functions," Mathematical Social Sciences, Elsevier, vol. 15(2), pages 135-143, April.
    5. Sholomov, Lev A., 2000. "Explicit form of neutral social decision rules for basic rationality conditions," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 81-107, January.
    6. Oloriz, Esteban & Candeal, Juan Carlos & Indurain, Esteban, 1998. "Representability of Interval Orders," Journal of Economic Theory, Elsevier, vol. 78(1), pages 219-227, January.
    7. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May.
    8. Herden, G., 1995. "On some equivalent approaches to Mathematical Utility Theory," Mathematical Social Sciences, Elsevier, vol. 29(1), pages 19-31, February.
    9. Banerjee, Asis & Pattanaik, Prasanta K., 1996. "A note on a property of maximal sets and choice in the absence of universal comparability," Economics Letters, Elsevier, vol. 51(2), pages 191-195, May.
    10. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
    11. Jaffray, Jean-Yves, 1975. "Semicontinuous extension of a partial order," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 395-406, December.
    12. Donaldson, David & Weymark, John A., 1998. "A Quasiordering Is the Intersection of Orderings," Journal of Economic Theory, Elsevier, vol. 78(2), pages 382-387, February.
    13. Diaye, Marc-Arthur, 1999. "Variable intervals model," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 21-33, July.
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    Cited by:

    1. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    2. Athanasios Andrikopoulos, 2019. "On the extension of binary relations in economic and game theories," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 277-285, June.
    3. Gianni Bosi & Asier Estevan, 2024. "Continuous Representations of Preferences by Means of Two Continuous Functions," Papers 2402.07908, arXiv.org.
    4. Gianni Bosi & Asier Estevan, 2020. "Continuous Representations of Interval Orders by Means of Two Continuous Functions," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 700-710, June.
    5. Athanasios Andrikopoulos, 2019. "A Generalization of Arrow’s Lemma on Extending a Binary Relation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2019, pages 1-6, April.
    6. repec:san:wpecon:1305 is not listed on IDEAS
    7. Andrikopoulos, Athanasios, 2009. "Szpilrajn-type theorems in economics," MPRA Paper 14345, University Library of Munich, Germany.
    8. Herden, Gerhard & Levin, Vladimir L., 2012. "Utility representation theorems for Debreu separable preorders," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 148-154.
    9. Alcantud, José Carlos R. & Díaz, Susana, 2013. "Szpilrajn-type extensions of fuzzy quasiorderings," MPRA Paper 50547, University Library of Munich, Germany.
    10. Athanasios Andrikopoulos, 2011. "Characterization of the existence of semicontinuous weak utilities for binary relations," Theory and Decision, Springer, vol. 70(1), pages 13-26, January.
    11. T. Demuynck, 2006. "Existence of closed and complete extensions applied to convex, homothetic an monotonic orderings," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/407, Ghent University, Faculty of Economics and Business Administration.
    12. Efe A. Ok & Gil Riella, 2014. "Topological Closure of Translation Invariant Preorders," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 737-745, August.
    13. Alcantud, José Carlos R. & Bosi, Gianni & Zuanon, Magalì, 2013. "Representations of preorders by strong multi-objective functions," MPRA Paper 52329, University Library of Munich, Germany.
    14. Bosi, Gianni & Campion, Maria J. & Candeal, Juan C. & Indurain, Esteban & Zuanon, Magali E., 2007. "Isotonies on ordered cones through the concept of a decreasing scale," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 115-127, September.
    15. Magyarkuti, Gyula, 2008. "Szeparábilitási koncepciók és a reprezentációs tétel Nachbin-féle megközelítése [Urishon-Nachbin approach to utility representation theorem]," MPRA Paper 20171, University Library of Munich, Germany.
    16. Athanasios Andrikopoulos, 2017. "Generalizations of Szpilrajn's Theorem in economic and game theories," Papers 1708.04711, arXiv.org.
    17. T. Demuynck, 2009. "Common ordering extensions," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 09/593, Ghent University, Faculty of Economics and Business Administration.

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