Hyperopic topologies on $l^{∞}$

Abstract

Myopic economic agents are well studied in economics. They are impatient. A myopic topology is a topology such that every continuous preference relation is myopic. If the space is \begin{document}$l^{∞}$\end{document} , the Mackey topology \begin{document}$τ _{M}(l^{∞},l^{1})$\end{document} , is the largest locally convex such topology. However there is a growing interest in patient consumers. In this paper we analyze the extreme case of consumers who only value the long run. We call such a consumer hyperopic. We define hyperopic preferences and hyperopic topologies. We show the existence of the largest locally convex hyperopic topology, characterize its dual and determine its relationship with the norm dual of \begin{document}$l^{∞}$\end{document} .