Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions

[1] AUMANN, R.: Utility theory without the completeness axiom, Econometrica 30 (1962), 445-462.10.2307/1909888Search in Google Scholar

[2] BACK, K.: Concepts of similarity for utility functions, J. Math. Econom. 15 (1986), 129-142.10.1016/0304-4068(86)90004-2Search in Google Scholar

[3] BOSI, G.-HERDEN, G.: The structure of completely useful and very useful topologies, 2006 (preprint).Search in Google Scholar

[4] BOSI, G.-HERDEN, G.: Continuous utility representations theorems in arbitrary concrete categories, Appl. Categ. Structures 16 (2008), 629-651.10.1007/s10485-007-9097-0Search in Google Scholar

[5] BOSI, G.-MEHTA, G. B.: Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof, J. Math. Econom. 38 (2002), 311-328.10.1016/S0304-4068(02)00058-7Search in Google Scholar

[6] BRIDGES, D. S.-MEHTA, G. B.: Representations of Preference Orderings, in: Lecture Notes in Econom. and Math. Systems, Vol. 422, Springer-Verlag, Berlin, 1995.10.1007/978-3-642-51495-1Search in Google Scholar

[7] CAMPI ´ON, M. J.-CANDEAL, J. C.-INDUR´AIN, E.: Semicontinuous orderrepresentability of topological spaces, Bol. Soc. Mat. Mexicana (3) 15 (2009), 81-90.Search in Google Scholar

[8] CANDEAL, J. C.-INDURAIN, E.-MEHTA, G. B.: Some utility theorems on inductive limits of preordered topological spaces, Bul. Austral. Math. Soc. 52 (1995), 235-246.10.1017/S0004972700014660Search in Google Scholar

[9] CASTAING, C.-RAYNAUD DE FITTE, P.-VALADIER, M.: Young Measures on Topological Spaces. With Applications in Control Theory and Probability Theory, in: Math. Appl., Vol. 571, Kluwer Academic Publ. Dordrecht, 2004.Search in Google Scholar

[10] CASTAING, C.-RAYNAUD DE FITTE, P.-SALVADORI, A.: Some variational convergence results with applications to evolution inclusions, in: Selected papers based on the presentation at the 3rd International Conference on Mathematical Analysis in Economic Theory (Sh. Kusuoka et al., eds.), Tokyo, Japan, 2004, Adv. Math. Econ., Vol. 8, Springer, Tokyo, 2006, pp. 33-73.10.1007/4-431-30899-7_2Search in Google Scholar

[11] CATERINO, A.-CEPPITELLI, R.-MACCARINO, F.: Continuous utility on hemicompact submetrizable k-spaces, Appl. Gen. Topol. 10 (2009), 187-195.10.4995/agt.2009.1732Search in Google Scholar

[12] CATERINO, A.-CEPPITELLI, R.-MEHTA, G. B.: Representations of topological preordered spaces, Math. Slovaca, 2008 (to appear).Search in Google Scholar

[13] CHATEAUNEUF, A.: Continuous representation of a preference relation on a connected topological space, J. Math. Econom. 16 (1987), 139-146.10.1016/0304-4068(87)90003-6Search in Google Scholar

[14] DEBREU, G.: Representation of a preference ordering by a numerical function, in: Decision Processes (R. Thrall, C. Coombs, R. Davies, eds.), Wiley, New York, 1954, pp. 159-166.Search in Google Scholar

[15] DEBREU, G.: Continuity properties of a Paretian utility, Internat. Econom. Rev. 5 (1964), 285-293.10.2307/2525513Search in Google Scholar

[16] EILENBERG, S.: Ordered topological spaces, Amer. J. Math. 63 (1941), 39-45.10.2307/2371274Search in Google Scholar

[17] ENGELKING, R.: General Topology. Rev. and Compl. Ed. . in: Sigma Ser. in Pure Math., Vol. 6, Heldermann Verlag, Berlin, 1989.Search in Google Scholar

[18] EST´EVEZ TORANZO,M.-HERV´ES BELOSO, C.: On the existence of continuous preference orderings without utility representations, J. Math. Econom. 24 (1995), 305-309.10.1016/0304-4068(94)00701-BSearch in Google Scholar

[19] FRANKLIN, S. P.-SMITH THOMAS, B. V.: A survey of kù-spaces, in: Proc. Topol. Conf., Baton Rouge, LA, 1977, Topology Proc., Vol. 2, Auburn Univ., Auburn, AL, 1978, pp. 111-124.Search in Google Scholar

[20] HERDEN, G.: On the existence of utility functions, Math. Soc. Sci. 17 (1989), 297-313.10.1016/0165-4896(89)90058-9Search in Google Scholar

[21] HERDEN, G.: Topological spaces for which every continuous total preorder can be represented by a continuous utility function, Math. Soc. Sci. 22 (1991), 123-136.10.1016/0165-4896(91)90002-9Search in Google Scholar

[22] HERDEN, G.-PALLACK, A.: Useful topologies and separable systems, Appl. Gen. Topol. 1 (2000), 61-82.10.4995/agt.2000.3024Search in Google Scholar

[23] HERDEN, G.-PALLACK, A.: On the continuous analogue of the Szpilrajn Theorem I, Math. Soc. Sci. 43 (2002), 115-134.10.1016/S0165-4896(01)00077-4Search in Google Scholar

[24] LEVIN, V. L.: A continuous utility theorem for closed preorders on a σ-compact metrizable space, Soviet Math. Dokl. 28 (1983), 715-718.Search in Google Scholar

[25] LUTZER, D. J.-BENNET, H. R.: Separability, the countable chain condition and the Lindel¨of property on linearly ordered spaces, Proc. Amer. Math. Soc. 23 (1969), 664-667.Search in Google Scholar

[26] MCCOY, R. A.: Functions spaces which are k-spaces, in: The Proceedings of the 1980 Topology Conference (J. Dydak et al., eds.), Topology Proc., Vol. 5, Auburn Univ., Auburn, AL, USA, 1980, pp. 139-146.Search in Google Scholar

[27] MEHTA, G. B.: Some general theorems on the existence of order-preserving functions, Math. Soc. Sci. 15 (1988), 135-143.10.1016/0165-4896(88)90018-2Search in Google Scholar

[28] MEHTA, G. B.: Preference and Utility. in: Handbook of Utility Theory, Vol. 1 (S. Barber´a et al., eds.), Kluwer Academic Publ., Dordrecht, 1988, pp. 1-47.Search in Google Scholar

[29] MONTEIRO, P. K.: Some results on the existence of utility functions on path connected spaces, J. Math. Econom. 16 (1987), 147-156.10.1016/0304-4068(87)90004-8Search in Google Scholar

[30] NACHBIN, L.: Topology and Order. Van Nostrand, Princeton, 1965.Search in Google Scholar

[31] OK, E. A.: Utility representation of an incomplete preference relation, J. Econom. Theory 104 (2002), 429-449.10.1006/jeth.2001.2814Search in Google Scholar

[32] OK, E. A.: Functional representation of rotund-valued proper multifunctions, New York University, 2002 (preprint).Search in Google Scholar

[33] PELEG, B.: Utility functions for partially ordered topological spaces, Econometrica 38 (1970), 93-96.10.2307/1909243Search in Google Scholar

[34] STEEN, L. A.-SEEBACH, J. A.: Counterexamples in Topology. Dover Publ., New York, 1995.Search in Google Scholar