Continuous utility on connected separable topological spaces

Continuous utility on connected separable topological spaces 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). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Economic Theory Bulletin Springer Journals

Continuous utility on connected separable topological spaces

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Society for the Advancement of Economic Theory
Subject
Economics; Economic Theory/Quantitative Economics/Mathematical Methods; Game Theory, Economics, Social and Behav. Sciences; Macroeconomics/Monetary Economics//Financial Economics; Public Finance
ISSN
2196-1085
eISSN
2196-1093
D.O.I.
10.1007/s40505-018-0149-4
Publisher site
See Article on Publisher Site

Abstract

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).

Journal

Economic Theory BulletinSpringer Journals

Published: Jun 6, 2018

References

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