International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 8, Pages 505-512
doi:10.1155/S0161171201007219

Orderability of topological spaces by continuous preferences.

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.