Topological conditions for the representation of preorders by continuous utilities

Authors

  • E. Minguzzi Università degli Studi di Firenze

DOI:

https://doi.org/10.4995/agt.2012.1640

Keywords:

Preorder normality, Utilities, Preorder representations, k-spaces

Abstract

We remove the Hausdorff condition from Levin's theorem on the representation of preorders by families of continuous utilities. We compare some alternative topological assumptions in a Levin's type theorem, and show that they are equivalent to a Polish space assumption.

Downloads

Download data is not yet available.

Author Biography

E. Minguzzi, Università degli Studi di Firenze

Dipartimento di Matematica Applicata "G. Sansone", Universitá degli Studi di Firenze, Via S. Marta 3, I-50139 Firenze, Italy

References

E. Akin and J. Auslander, Generalized recurrence, compactifications and the Lyapunov topology, Studia Mathematica 201 (2010), 49–63. http://dx.doi.org/10.4064/sm201-1-4

R. F. Arens, A topology for spaces of transformations, Ann. of Math. 47 (1946), 480–495. http://dx.doi.org/10.2307/1969087

N. Bourbaki, Elements of Mathematics: General topology I, Reading: Addison-Wesley Publishing (1966).

D. S. Bridges and G. B. Mehta, Representations of preference orderings, vol. 442 of Lectures Notes in Economics and Mathematical Systems. Berlin: Springer-Verlag (1995).

A. Caterino, R. Ceppitelli and F. Maccarino, Continuous utility functions on submetrizable hemicompact k-spaces, Applied General Topology 10 (2009), 187–195.

O. Echi and S. Lazaar, Quasihomeomorphisms and lattice equivalent topological spaces, Applied General Topology 10 (2009), 227–237.

R. Engelking, General Topology, Berlin: Helderman Verlag (1989).

O. Evren and E. A. Ok, On the multi-utility representation of preference relations, J. Math. Econ. 47 (2011), 554–563. http://dx.doi.org/10.1016/j.jmateco.2011.07.003

S. T. Franklin and B. V. Smith Thomas, A survey of kω-spaces, Topology Proceedings 2 (1977), 111–124.

G. Herden and A. Pallack, On the continuous analogue of the Szpilrajn theorem I, Mathematical Social Sciences 43 (2002), 115–134. http://dx.doi.org/10.1016/S0165-4896(01)00077-4

Y. Kai-Wing, Quasi-homeomorphisms and lattice-equivalences of topological spaces, J. Austral. Math. Soc. 14 (1972), 41–44. http://dx.doi.org/10.1017/S1446788700009617

J. L. Kelley, General Topology, New York: Springer-Verlag (1955).

H.-P. A. Künzi and T. A. Richmond, Ti-ordered reflections, Applied General Topology 6 (2005), 207–216.

J. D. Lawson, Order and strongly sober compactifications, Oxford: Clarendon Press, vol. Topology and Category Theory in Computer Science, pages 171–206 (1991).

V. L. Levin, A continuous utility theorem for closed preorders on a σ-compact metrizable space, Soviet Math. Dokl. 28 (1983), 715–718.

E. Minguzzi, Time functions as utilities, Commun. Math. Phys. 298 (2010), 855–868. http://dx.doi.org/10.1007/s00220-010-1048-1

E. Minguzzi, Normally preordered spaces and utilities, Order (2011), http://dx.doi.org/10.1007/s11083-011-9230-4

L. Nachbin, Topology and order, Princeton: D. Van Nostrand Company, Inc. (1965).

L. A. Steen and J. A. Seebach, Jr., Counterexamples in topology, New York: Holt, Rinehart and Winston, Inc. (1970).

N. E. Steenrod, A convenient category of topological spaces, Michigan Math. J. 14 (1967), 133–152. http://dx.doi.org/10.1307/mmj/1028999711

S. Willard, General topology, Reading: Addison-Wesley Publishing Company (1970).

Downloads

Published

2012-04-15

How to Cite

[1]
E. Minguzzi, “Topological conditions for the representation of preorders by continuous utilities”, Appl. Gen. Topol., vol. 13, no. 1, pp. 81–89, Apr. 2012.

Issue

Section

Articles