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# Topological spaces for which every closed and semi-closed preorder respectively admits a continuous multi-utility representation

## Author

Listed:
• Bosi, Gianni
• Herden, Gerhard

## Abstract

On basis of the meanwhile classical continuous multi-utility representation theorem of Levin on locally compact and $\sigma$-compact Hausdorff-spaces the question of characterizing all topological spaces $(X,t)$ for which every closed and semi-closed preorder respectively admits a continuous multi-utility representation will be discussed. In this way we are able to provide the fundaments of a purely topological theory that systematically combines topological and order theoretic aspects of the continuous multi-utility representation problem.

## Suggested Citation

• Bosi, Gianni & Herden, Gerhard, 2014. "Topological spaces for which every closed and semi-closed preorder respectively admits a continuous multi-utility representation," MPRA Paper 53404, University Library of Munich, Germany.
• Handle: RePEc:pra:mprapa:53404
as

File URL: https://mpra.ub.uni-muenchen.de/53404/1/MPRA_paper_53404.pdf
File Function: original version

## References listed on IDEAS

as
1. Herden, G., 1989. "On the existence of utility functions," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 297-313, June.
2. Herden, G., 1989. "On the existence of utility functions ii," Mathematical Social Sciences, Elsevier, vol. 18(2), pages 107-117, October.
3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
4. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
5. Pivato, Marcus, 2013. "Multiutility representations for incomplete difference preorders," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 196-220.
6. Herden, G. & Mehta, G. B., 2004. "The Debreu Gap Lemma and some generalizations," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 747-769, November.
7. Galaabaatar, Tsogbadral & Karni, Edi, 2012. "Expected multi-utility representations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 242-246.
8. Özgür Evren, 2008. "On the existence of expected multi-utility representations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 575-592, June.
9. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
Full references (including those not matched with items on IDEAS)

### Keywords

Normal preorder; strongly normal preorder sep paracompact space; Lindelof space; metrizable space;

### JEL classification:

• C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

### NEP fields

This paper has been announced in the following NEP Reports:

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