International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2001 / Article

Open Access

Volume 27 |Article ID 680516 | https://doi.org/10.1155/S0161171201007219

José Carlos Rodríguez Alcantud, "Orderability of topological spaces by continuous preferences", International Journal of Mathematics and Mathematical Sciences, vol. 27, Article ID 680516, 8 pages, 2001. https://doi.org/10.1155/S0161171201007219

Orderability of topological spaces by continuous preferences

Received13 Mar 2001

Abstract

We extend van Dalen and Wattel's (1973) characterization of orderable spaces and their subspaces by obtaining analogous results for two larger classes of topological spaces. This type of spaces are defined by considering preferences instead of linear orders in the former definitions, and possess topological properties similar to those of (totally) orderable spaces (cf. Alcantud, 1999). Our study provides particular consequences of relevance in mathematical economics; in particular, a condition equivalent to the existence of a continuous preference on a topological space is obtained.

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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