Numerical representation for lower quasi-continuous preferences
A weaker than usual continuity condition for acyclic preferences is introduced. For preorders this condition turns out to be equivalent to lower continuity, but in general this is not true. By using this condition, a numerical representation which is upper semicontinuous is obtained. This fact guarantees the existence of maxima of such a function, and therefore the existence of maximal elements of the binary relation.
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- Tian, Guoqiang & Zhou, Jianxin, 1995. "Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 281-303.
- Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
- Peris, Josep E. & Subiza, Begona, 1995. "A weak utility function for acyclic preferences," Economics Letters, Elsevier, vol. 48(1), pages 21-24, April.
- Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
- Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
- Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
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