Existence of a semicontinuous or continuous utility function: A unified approach and an elementary proof

Journal of Mathematical Economics

Volumn 38, Issue 3, 2002, Pages 311-328

  Bosi, G ^a   Mehta, G B ^b  

^a UNIVERSITY OF TRIESTE   (Italy)

^b UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Decreasing scale; Generalized urysohn system; Preordered bitopological space; Utility function

Indexed keywords

EID: 0036847596     PISSN: 03044068     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4068(02)00058-7     Document Type: Article

References (33)

1. Beardon, A.F., 1992. Debreu's Gap Theorem. Economic Theory 2, 150-152.
2. Beardon, A.F., 1994. Utility theory and continuous monotonic functions. Economic Theory 4, 531-538.
3. Beardon, A.F., Mehta, G.B., 1994. The utility theorems of Wold, Debreu and Arrow-Hahn. Econometrica 62, 181-186.
4. Bewley, T., 1972. Existence of equilibria in economies with infinitely many commodities. Journal of Economic Theory 4, 514-540.
5. Bosi, G., 1996. A note on the existence of semicontinuous order-preserving functions. Paper Presented at the Mini-Conference on Mathematical Utility Theory, Essen, Germany, 22-24 October 1997.
6. Bosi, G., Isler, R., 2001. Continuous representability of complete preorders on the space of upper-continuous capacities. Applied General Topology 2, 27-31.
7. Bridges, D.S., Mehta, G.B., 1995. Representations of Preference Orderings. Springer-Verlag, Berlin.
8. Burgess, D.C.J., Fitzpatrick, M., 1977. On separation axioms in topological preordered spaces. Mathematical Proceedings of the Cambridge Philosophical Society 82, 59-65.
9. Debreu, G., 1954. Representation of a preference ordering by a numerical function. In: Thrall, R., Coombs, C.C., Davis, R. (Eds.), Decision Processes. Wiley, New York, pp. 159-166.
10. Debreu, G., 1964. Continuity properties of paretian utility. International Economic Review 5, 285-293.
11. Devlin, K., 1979. Fundamentals of Contemporary Set Theory. Springer, Berlin.
12. Engelking, R., 1977. General Topology. Polish Scientific Publishers, Warsaw.
13. Herden, G., 1989. On the existence of utility functions. Mathematical Social Sciences 17, 297-313.
14. Herden, G., Mehta, G.B., 1995. Semicontinuous Order Preserving Functions, preprint.
15. Herden, G., Mehta, G.B., 1996. Open gaps, metrization and utility. Economic Theory 7, 541-546.
16. Herden, G., Mehta, G.B., 2001. Is the Debreu Gap Lemma Generalizable ?, preprint.
17. Hrbacek, K., Jech, T., 1999. Introduction to Set Theory. Marcel Dekker, New York.
18. Isler, R., 1997. Semicontinuous utility functions in topological spaces. Rivista di Matematica per le Scienze Economiche eSociali 20, 111-116.
19. Jaffray, J., 1975. Existence of a continuous utility function: an elementary proof. Econometrica 43, 981-983.
20. Jones, L.E., 1984. A competitive model of commodity differentiation. Econometrica 52, 507-530.
21. Kamke, E., 1950. Theory of Sets. Dover, New York.
22. Mas-Colell, A., 1975. A model of equilibrium with differentiated commodities. Journal of Mathematical Economics 2, 263-295.
23. Mehta, G.B., 1988. Some general theorems on the existence of order-preserving functions. Mathematical Social Sciences 15, 135-146.
24. Mehta, G.B., 1997. A remark on a utility representation theorem of Rader. Economic Theory 9, 367-370.
25. Mehta, G.B., 1998. Preference and utility. In: Barberá, S., Hammond, P., Seidl, C. (Eds.), Handbook of Utility Theory, vol. 1. Kluwer Academic Publishers, Dordrecht, pp. 1-47.
26. Munkres, J., 2000. Topology, 2nd ed. Prentice-Hall, New York.
27. Nachbin, L., 1965. Topology and Order. D. Van Nostrand and Company, New York.
28. Newman, M.H.A., 1992. Elements of the Topology of Plane Sets of Points. Dover, New York.
29. Peleg, B., 1970. Utility functions for partially ordered topological spaces. Econometrica 38, 93-96.
30. Rader, T., 1963. The existence of a utility function to represent preferences. Review of Economic Studies 30, 229-232.
31. Rosenstein, J., 1982. Linear Orderings. Academic Press, New York.
32. Toussaint, S., 1984. On the existence of equilibria in economies with infinitely many commodities and without ordered preferences. Journal of Economic Theory 33, 98-115.
33. Ward, A.J., 1935. The topological characterisation of an open linear interval. Proceedings of the London Mathematical Society 4, 191-198.