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Some utility theorems on inductive limits of preordered topological spaces

Published online by Cambridge University Press:  17 April 2009

J.C. Candeal
Affiliation:
Departamento de Análisis Económico, Universidad de Zaragoza, Facultad de Ciencias Económicas, y Empresariales, Gran Vía 2–4, 50005-Zaragoza, Spain
E. IndurÁIn
Affiliation:
Departamento de Matemática e Informática, Universidad Pública de Navarra, Campus Arrosadía s.n. 31006-Pamplona, Spain
G.B. Mehta
Affiliation:
Department of Economics, The University of Queensland, St. Lucia, Queensland, Australia 4067
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Abstract

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We prove the existence of an order-preserving function on a class of preordered topological spaces that are inductive limits of preordered spaces. Some applications to economics are given.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Aliprantis, C.D., Brown, D.J. and Burkinshaw, O., Existence and optimality of competitive equilibria (Springer-Verlag, Berlin, Heidelberg, New York, 1990).CrossRefGoogle Scholar
[2]Arrow, K.J. and Hahn, F.H., General competitive analysis (Holden Day, San Francisco, 1971).Google Scholar
[3]Aumann, R.J., ‘Subjective programming’, in Human Judgements and Optimality, (Shelly, M.W. II, and Bryan, G.L., Editors) (John Wiley and Sons, New York, 1964).Google Scholar
[4]Candeal, J.C. and Induráin, E., ‘Sobre caracterizaciones topológicas de la representabilidad de cadenas mediante funciones de utilidad’, Revista Espan¯ola de Economía 7 (2) (1990), 235244.Google Scholar
[5]Candeal, J.C. and Induráin, E., ‘Representación numérica de órdenes totales’, Rev. Real Acad. Cienc. Exact. Fis. Natur. Madrid 84 (1990), 415428.Google Scholar
[6]Croom, F., Principles of topology (Saunders College Publishing, Philadelphia, 1989).Google Scholar
[7]Debreu, G., ‘Representation of a preference ordering by a numerical function’, in Decision processes, (Thrall, R. et al. , Editors) (John Wiley and Sons, New York, 1954), pp. 159166.Google Scholar
[8]Dugundji, J., Topology (Allyn and Bacon, Boston, 1966).Google Scholar
[9]Eilenberg, S., ‘Ordered topological spaces’, Amer. J. Math. 63 (1941), 3945.CrossRefGoogle Scholar
[10]Fleischer, I., ‘Numerical representation of utility’, J. Soc. Indust. Appl. Math. 9 (1961), 4850.CrossRefGoogle Scholar
[11]Herden, G., ‘On the existence of utility functions’, Math. Social Sci. 17 (1989), 297313.CrossRefGoogle Scholar
[12]Herden, G., ‘On the existence of utility functions II’, Math. Social Sci. 18 (1989), 107117.CrossRefGoogle Scholar
[13]Herden, G., ‘Some lifting theorems for continuous utility functions’, Math. Social Sci. 18 (1989), 119134.CrossRefGoogle Scholar
[14]Holmes, R., Geometric functional analysis and its applications (Springer-Verlag, Berlin, Heidelberg, New York, 1975).CrossRefGoogle Scholar
[15]Jaffray, J.Y., ‘Existence of a continuous utility function: an elementary proof’, Econometrica 43 (1975), 981983.CrossRefGoogle Scholar
[16]Levin, V.L., ‘Measurable utility theorems for closed and lexicographic preference relations’, Soviet Math. Dokl. 27 (3) (1983), 639643.Google Scholar
[17]Levin, V.L., ‘General Monge-Kantorovich problem and its applications in measure theory and mathematical economies’, in Functional Analysis, Optimization and Mathematical Economics, (Leifman, Lev J., Editor) (Oxford University Press, 1990).Google Scholar
[18]Mas-Colell, A, ‘An equilibrium existence theorem without complete or transitive preferences’, J. Math. Econom. 1 (1974), 237246.CrossRefGoogle Scholar
[19]Mehta, G.B., ‘A new extension procedure for the Arrow-Hahn theorem’, Internat. Econom. Rev. 22 (1981), 113118.CrossRefGoogle Scholar
[20]Mehta, G.B., ‘On a theorem of Fleischer’, J. Austral. Math. Soc. Ser. A 40 (1986), 261266.CrossRefGoogle Scholar
[21]Mehta, G.B., ‘Existence of an order-preserving function on normally preordered spaces’, Bull. Austral. Math. Soc. 34 (1986), 141147.CrossRefGoogle Scholar
[22]Nachbin, L., Topology and order (Van Nostrand, Princeton, N.J., 1965).Google Scholar
[23]Peleg, B., ‘Utility functions for partially ordered topological spaces’, Econometrica 38 (1970), 9396.CrossRefGoogle Scholar
[24]Rudin, W., Real and complex analysis (McGraw-Hill, New York, 1966).Google Scholar
[25]Schmeidler, D., ‘Competitive equilibria in markets with a continuum of traders and incomplete preferences’, Econometrica 37 (1969), 568585.CrossRefGoogle Scholar
[26]Swartz, C., Introduction to functional analysis (Marcel Dekker, New York, 1992).Google Scholar
[27]Tennison, B.R., Sheaf theory (Cambridge University Press, Cambridge, U.K., 1975).CrossRefGoogle Scholar