Orderability of topological spaces by continuous preferences. (Q5957236)

Summary: We extend a characterization of \textit{J. van Dalen} and \textit{E. Wattel} [Gen. Topol. Appl. 3, 347--354 (1973; Zbl 0272.54026)] of orderable spaces and their subspaces by obtaining analogous results for two larger classes of topological spaces. This type of space is defined by considering preferences instead of linear orders in the earlier definitions, and possesses topological properties similar to those of (totally) orderable spaces [cf. \textit{J. C. R. Alcantud}, Int. J. Math. Math. Sci. 22, No. 1, 17--27 (1999; Zbl 0924.06016)]. 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.