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ON YI'S EXTENSION PROPERTY FOR TOTALLY PREORDERED TOPOLOGICAL SPACES

  • CAMPION M.J. (Universidad Publica de Navarra Departmento de Matematica e Informatica Campus Arrosadia) ;
  • CANDEAL J.C. (Universidad de Zaragoza Facultad de Ciencias Economicas y Empresariales Departamento de Analisis Economico) ;
  • INDURAIN ESTEBAN (Universidad Publica de Navarra Departamento de Matematica e Informatica Campus Arrosadia)
  • Published : 2006.01.01

Abstract

The objective of this paper is to show further results concerning the problem of extending total preorders from a subset of a topological space to the entire space using the approach introduced by Gyoseob Yi.

Keywords

References

  1. Ch. D. Aliprantis and K. C. Border, Infinite dimensional Analysis, A Hitch- hicker's guide, Springer, Berlin, 1999
  2. A. F. Beardon, J. C. Candeal, G. Herden, E. Indurain, and G. B. Mehta,, The non-existence of a utility function and the structure of non-representable preference relations, J. Math. Econom. 37 (2002), no. 1, 17-38 https://doi.org/10.1016/S0304-4068(02)00003-4
  3. G. Birkhoff, Lattice theory(Third edition), American Mathematical Society, Providence, RI, 1967
  4. G. Bosi and G. Herden, On the structure of completely useful topologies, Appl. Gen. Topol. 3 (2002), no. 2, 145-167 https://doi.org/10.4995/agt.2002.2060
  5. D. S. Bridges and G. B. Mehta, Representation of preference orderings, Springer-Verlag, Berlin, 1995
  6. J. C. Candeal, C. Herves, and E. Indurain, Some results on representation and extension of preferences, J. Math. Econom. 29 (1998), no. 1, 75-81 https://doi.org/10.1016/S0304-4068(97)00005-0
  7. J. C. Candeal, E. Indurain, and G. B. Mehta, Some utility theorems on inductive limits of preordered topological spaces, Bull. Austral. Math. Soc. 52 (1995), no. 2, 235-246 https://doi.org/10.1017/S0004972700014660
  8. J. C. Candeal, E. Indurain, and G. B. Mehta, Utility functions on locally connected spaces, J. Math. Econom. 40 (2004), no. 6, 701-711 https://doi.org/10.1016/S0304-4068(03)00085-5
  9. H. H. Corson, The weak topology of a Banach space, Trans. Amer. Math. Soc. 101 (1961), 1-15 https://doi.org/10.2307/1993408
  10. G. Debreu, Representation of a preference ordering by a numerical function, In: Thrall, R., Coombs, C. and R. Davies (eds.), Decision Processes, John Wiley, New York, 1954, 159-166
  11. J. Dugundji, Topology, Allyn and Bacon, Boston, 1966
  12. S. Eilenberg, Ordered topological spaces, Amer. J. Math. 63 (1941), 39-45 https://doi.org/10.2307/2371274
  13. R. Engelking, General Topology. Revised and completed edition, Heldermann Verlag, Berlin, 1989
  14. M. Estevez and C. Herves, On the existence of continuous preference orderings without utility representations, J. Math. Econom. 24 (1995), 305-309 https://doi.org/10.1016/0304-4068(94)00701-B
  15. G. Herden, Some lifting theorems for continuous utility functions, Math. Social Sci. 18 (1989), no. 2, 119-134 https://doi.org/10.1016/0165-4896(89)90042-5
  16. G. Herden, Topological spaces for which every continuous total preorder can be represented by a continuous utility function, Math. Social Sci. 22 (1991), no. 2, 123-126 https://doi.org/10.1016/0165-4896(91)90002-9
  17. G. Herden and A. Pallack, Useful topologies and separable systems, Appl. Gen. Topol. 1 (2000), no. 1, 61-82 https://doi.org/10.4995/agt.2000.3024
  18. R. Isler, Semicontinuous utility functions in topological spaces, Rivista di Mate-matica per le Scienze economiche e sociali 20 (1997), no. 1, 111-116 https://doi.org/10.1007/BF02688992
  19. P. K. Monteiro, Some results on the existence of utility functions on path connected spaces, J. Math. Econom. 16 (1987), 147-156 https://doi.org/10.1016/0304-4068(87)90004-8
  20. L. Nachbin, Topology and Order, Van Nostrand, New York, 1965
  21. A. Pelczynski, Projections in certain Banach spaces, Studia Math. 19 (1960), 209-228 https://doi.org/10.4064/sm-19-2-209-228
  22. T. Rader, The existence of a utility function to represent preferences, Review of Economic Studies 30 (1963), 229-232 https://doi.org/10.2307/2296323
  23. L. A. Steen and J. A. Jr. Seebach, Counterexamples in Topology, Dover Publications, Mineola, NY, 1995
  24. E. Szpilrajn-Marczewski, Remarque sur les produits cartesiens d'espaces topologiques, C.R.(Doklady) Acad. Sci. URSS 31 (1941), 525-527
  25. G. Yi, Continuous extensions of preferences, J. Math. Econom. 22 (1993), 547-555 https://doi.org/10.1016/0304-4068(93)90003-4

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