Econ Theory Bull https://doi.org/10.1007/s40505-018-0149-4 RESEARCH ARTICLE Continuous utility on connected separable topological spaces Yann Rébillé Received: 3 October 2017 / Accepted: 31 May 2018 © Society for the Advancement of Economic Theory 2018 Abstract The elaboration of utility theory takes back its source in early economic theory. Despite an obvious practical use for applications and an intuitive appeal, utility theory relies on sophisticated abstract mathematics such as topology. Our interest is primarily on Debreu–Eilenberg’s theorem. On connected separable topological spaces continuous total preorders admit continuous utility representations. We provide a sim- ple proof and derive related results. Keywords Continuous utility · Preferences representation · Total preorder · Topological space JEL classiﬁcation C60 · D60 · D11 1 Introduction Utility functions constitute a basic starter for a ﬁrst course in microeconomics. They provide numerical representations of preferences. The elaboration of utility theory takes back its source in early economic theory (see Stigler’s historical analysis of utility theory Stigler 1950a, b). Despite an obvious practical use for applications and an intuitive appeal, utility theory relies on sophisticated abstract mathematics (set the- ory, topology). Our interest is primarily on Debreu–Eilenberg’s theorem on connected separable topological spaces (in Debreu 1954, 1964; Eilenberg 1941).
Economic Theory Bulletin – Springer Journals
Published: Jun 6, 2018
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