The questionnaire topology on some spaces of economic preferences
type: Item
instance of: scholarly article
title: The questionnaire topology on some spaces of economic preferences
zbMATH Open document ID: 0791.90005
DOI: 10.1016/0304-4068(93)90038-M
author: James Redekop
published in: Journal of Mathematical Economics
publication date: 1994-07-13T00:00:00Z
review text: We define and characterize two well-known topologies on spaces of preferences, namely the Kannai and closed-convergence topologies. We show that on spaces of economic preferences (e.g. continuous and monotonic preferences on \(\mathbb{R}^ l_ +\)), both topologies coincide and have an especially simple characterization. Namely, they agree with the questionnaire topology, which takes as a base the set of questionnaire sets \(Q((x_ 1,y_ 1),\dots(x_ n,y_ n))=\bigcap^ n_{i=1}\{p| x_ i\widehat py_ i\}\), where \(\widehat p\) denotes strict preference. The characterization permits the statement and proof of some theorems on the innocuousness of the assumption of continuity, given monotonicity or convexity; and it allows for dramatically simplified proofs of some denseness results resembling those of \textit{Y. Kannai} [J. Math. Econ. 1, 101-106 (1974; Zbl 0288.90011)], \textit{A. Mas- Colell} [J. Econ. Theory 8, 305-320 (1974)] and \textit{A. Araujo} [J. Math. Econ. 14, 61-66 (1985; Zbl 0582.90013)].
Mathematics Subject Classification ID: 91B08
zbMATH DE Number: 458841
zbMATH Keywords: Kannai topology
zbMATH Keywords: closed-convergence topologies
zbMATH Keywords: spaces of economic preferences
zbMATH Keywords: questionnaire topology
MaRDI profile type: Publication
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full work available at URL: 0304-4068(93)90038-m
OpenAlex ID: W2026262731
description: scientific article; zbMATH DE number 458841