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On a theorem of Fleischer

Part of: Special properties

Published online by Cambridge University Press:  09 April 2009

G. Mehta
G. Mehta
Affiliation:
Departments of Economics and of Mathematics, University of Queensland, St. Lucia, Queensland, 4067, Australia
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Abstract

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Fleischer proved that a linearly ordered set that is separable in its order topology and has countably many jumps is order-isomorphic to a subset of the real numbers. The object of this paper is to extend Fleischer's result and to prove it in a different way. The proof of the theorem is based on Nachbin's extension to ordered topological spaces of Urysohn's separation theorem in normal topological spaces.

MSC classification

Secondary: 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 2 , April 1986 , pp. 261 - 266
Copyright
Copyright Australian Mathematical Society 1986

References

1Debreu, G., Representation of a preference ordering by a numerical function, pp. 159166Decision processes, Thrall, R., Coombs, C. and Davis, R. eds. (Wiley, New York, 1954).Google Scholar
2Eilenberg, S., Ordered topological spaces, Amer. J. Math. 63 (1941), 3945.CrossRefGoogle Scholar
3Fishburn, P., Utility theory for decision making (Wiley, New York, 1970).CrossRefGoogle Scholar
4Fleischer, I., Numerical representation of utility, Siam J. 9 (1961), 4850.Google Scholar
5Mehta, G., Existence of an order-preserving function on normally preordered spaces, Bull. Austral. Math. Soc., to appear.Google Scholar
6Mehta, G., Toplogical ordered spaces and utility functions, Internat. Econom. Rev. 18 (1977), 779782.CrossRefGoogle Scholar
7Mehta, G., Recent developments in utility theory, Indian Econom. J. 30 (1983), 103125.Google Scholar
8Mehta, G., Ordered topological spaces and the theorems of Debreu and Peleg, Indian J. Pure and Appl. Math. 14 (1983), 11741182.Google Scholar
9Mehta, G., On a theorem of Peleg, Indian J. Pure and Appl. Math., to appear.Google Scholar
10Nachbin, L., Topology and order (D. Van Nostrand Company, Princeton, New Jersey, 1965).Google Scholar
11Peleg, B., Utility functions for partially ordered topological spaces, Econometrica 38 (1970), 9396.CrossRefGoogle Scholar
12Richter, M., Revealed preference theory, Econometrica 34 (1966), 635645.CrossRefGoogle Scholar
13Roberts, F., Measurement theory with applications to decision making, utility, and the social sciences (Encyclopedia of Mathematics and its Applications, Volume 7, Addison-Wesley Publishing Company, 1979).Google Scholar