| Abstract: | We consider the problem of extending preferences from a subset of a commodity space to the entire space. It is a simple consequence of the Tietze extension theorem that continuous preferences can be extended if they are defined on closed subsets of a normal space and are representable by utility functions. We show the following: If the space is a non-separable metric space, then extension of preferences is not always possible. In fact for (path-connected) metric spaces, extension property, utility representation property, and separability are equivalent to each other. |
