The theory of consumer's choice often includes as one of its axioms the existence of a transitive preference relation defined on some commodity space X. In this paper I prove that the transitivity of preference can be deduced from purely topological assumptions on certain sets, defined by preference, in the commodity space. Moreover, these topological assumptions are in no way unusual, and, with one exception, are a part of the existing literature on utility theory. 2 The remainder of the paper is devoted to one rather technical theorem, and several examples designed to illustrate how the theorems presented break down when one or more of the assumptions under which they were proved are violated.
展开▼
