International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 8, Pages 505-512
Orderability of topological spaces by continuous preferences
Facultad de Economia Y Empresa, Universidad de Salamanca, Salamanca 37008, Spain
Received 13 March 2001
Copyright © 2001 José Carlos Rodríguez Alcantud. 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.
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.