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Normally Preordered Spaces and Utilities

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Abstract

In applications it is useful to know whether a topological preordered space is normally preordered. It is proved that every k ω -space equipped with a closed preorder is a normally preordered space. Furthermore, it is proved that second countable regularly preordered spaces are perfectly normally preordered and admit a countable utility representation.

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References

  1. Akin, E.: The general topology of dynamical systems. Amer. Math. Soc., Providence (1993)

  2. Aumann, R.J.: Utility theory without the completeness axiom. Econometrica 30, 445–462 (1962)

    Article  MATH  Google Scholar 

  3. Bosi, G., Herden, G.: On a possible continuous analogue of the Szpilrajn theorem and its strengthening by Dushnik and Miller. Order 23, 271–296 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bosi, G., Isler, R.: Continuous utility functions for nontotal preorders: a review of recent results, vol. 257. Preferences and Decisions of Studies in Fuzziness and Soft Computing, pp. 1–10. Springer-Verlag (2010)

  5. Bourbaki, N.: Elements of Mathematics: General Topology I. Reading: Addison-Wesley Publishing (1966)

    Google Scholar 

  6. Bridges, D.S., Mehta, G.B.: Representations of preference orderings, vol. 442. Lectures Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin (1995)

    MATH  Google Scholar 

  7. Candeal-Haro, J.C., Induráin, E., Mehta, G.B.: Some utility theorems on inductive limits of preordered topological spaces. Bull. Aust. Math. Soc. 52, 235–246 (1995)

    Article  Google Scholar 

  8. Engelking, R.: General Topology. Helderman Verlag, Berlin (1989)

    MATH  Google Scholar 

  9. Evren, O., Ok, E.A.: On the multi-utility representation of preference relations. https://files.nyu.edu/eo1/public/Papers-PDF/MU4.pdf (2008). Accessed 27 Aug 2011

  10. Fletcher, P., Lindgren, W.: Quasi-uniform spaces, Lect. Notes in Pure and Appl. Math., vol. 77. Marcel Dekker, Inc., New York (1982)

    MATH  Google Scholar 

  11. Franklin, S.T., Smith Thomas, B.V.: A survey of k ω -spaces. Topol. Proc. 2, 111–124 (1977)

    Google Scholar 

  12. Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M.W., Scott, D.S.: Continuous Lattices and Domains. Cambridge University Press (2003)

  13. Herden, G.: On the existence of utility functions. Math. Soc. Sci. 17, 297–313 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  14. Herden, G., Pallack, A.: On the continuous analogue of the Szpilrajn theorem I. Math. Soc. Sci. 43, 115–134 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kelley, J.L.: General Topology. Springer-Verlag, New York (1955)

    MATH  Google Scholar 

  16. Kopperman, R. and Lawson, J.: Bitopological and topological ordered k-spaces. Topol. Its Appl. 146–147, 385–396 (2005)

    Article  MathSciNet  Google Scholar 

  17. Künzi, H.-P.A.: Completely regular ordered spaces. Order 7, 283–293 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  18. Künzi, H.-P.A., Watson, S.: A metrizable completely regular ordered space. Comment. Math. Univ. Carol. 35, 773–778 (1994)

    MATH  Google Scholar 

  19. Lawson, J., Madison, B.: On congruences of cones. Math. Z. 120, 18–24 (1971)

    Article  MathSciNet  Google Scholar 

  20. Levin, V.L.: A continuous utility theorem for closed preorders on a σ-compact metrizable space. Sov. Math. Dokl. 28, 715–718 (1983)

    MATH  Google Scholar 

  21. Levin, V. L.: Measurable utility theorem for closed and lexicographic preference relations. Sov. Math. Dokl. 27, 639–643 (1983)

    MATH  Google Scholar 

  22. Levin, V.L., Milyutin, A.A.: The problem of mass transfer with a discontinuous cost function and a mass statement of the duality problem for convex extremal problems. Russ. Math. Surv. 34, 1–78 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  23. McCallion, T.: Compactifications of ordered topological spaces. Proc. Camb. Philol. Soc. 71, 463–473 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  24. McCartan, S.D.: Separation axioms for topological ordered spaces. Proc. Camb. Philol. Soc. 64, 965–973 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  25. Mehta, G.: Some general theorems on the existence of order-preserving functions. Math. Soc. Sci. 15, 135–143 (1988)

    Article  MATH  Google Scholar 

  26. Milnor, J.: Construction of universal bundles, I. Ann. Math. 63, 272–284 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  27. Minguzzi, E.: Time functions as utilities. Commun. Math. Phys. 298, 855–868 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  28. Minguzzi, E.: Normally preordered spaces and utilities. arXiv:1106.4457v2 (2011)

  29. Morita, K.: On the decomposition spaces of locally compact spaces. Proc. Jpn. Acad. 32, 544–548 (1956)

    Article  MATH  Google Scholar 

  30. Nachbin, L.: Topology and Order. D. Van Nostrand Company, Inc., Princeton (1965)

    MATH  Google Scholar 

  31. Ok, E.A.: Utility representation of an incomplete preference relation. J. Econ. Theory 104, 429–449 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  32. Priestley, H.A.: Ordered topological spaces and the representation of distributive lattices. Proc. Lond. Math. Soc. 24, 507–530 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  33. Willard, S.: General topology. Reading: Addison-Wesley Publishing Company (1970)

    MATH  Google Scholar 

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  1. Dipartimento di Matematica Applicata “G. Sansone”, Università degli Studi di Firenze, Via S. Marta 3, 50139, Firenze, Italy

    Ettore Minguzzi

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  1. Ettore Minguzzi
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Minguzzi, E. Normally Preordered Spaces and Utilities. Order 30, 137–150 (2013). https://doi.org/10.1007/s11083-011-9230-4

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