International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 1, Pages 17-27
Topological properties of spaces ordered by preferences
Facultad de Economia y Empresa, Universidad de Salamanca, Salamanca E 37008 , Spain
Received 24 April 1997; Revised 22 November 1997
Copyright © 1999 J. C. R. 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.
In this paper, we analyze the main topological properties of a
relevant class of topologies associated with spaces ordered by preferences
(asymmetric, negatively transitive binary relations). This class consists
of certain continuous topologies which include the order topology. The
concept of saturated identification is introduced in order to provide a
natural proof of the fact that all these spaces possess topological
properties analogous to those of linearly ordered topological spaces,
inter alia monotone and hereditary normality, and complete regularity.