The Euclidean distance construction of order homomorphisms
type: Item
instance of: scholarly article
title: The Euclidean distance construction of order homomorphisms
zbMATH Open document ID: 0641.90015
DOI: 10.1016/0165-4896(88)90021-2
author: Douglas Bridges
published in: Mathematical Social Sciences
publication date: 1988-01-01T00:00:00Z
review text: The Euclidean distance technique of Arrow and Hahn is used to construct an upper semicontinuous order homomorphism (partial utility function) from (X,\(\succ)\) to \(({\mathbb{R}},>)\), where X is a closed, convex subset of \({\mathbb{R}}^ N\) and \(\succ\) is a continuous strict partial order on X. It is also shown that the order homomorphism is upper semicontinuous as a function on \(X\times {\mathcal P}(X)\), where \({\mathcal P}(X)\) is the set of continuous strict partial orders on X, taken with the topology of closed convergence.
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 06A99
zbMATH DE Number: 4045438
zbMATH Keywords: strict upper contour set
zbMATH Keywords: joint continuity
zbMATH Keywords: Euclidean distance technique
zbMATH Keywords: upper semicontinuous order homomorphism
zbMATH Keywords: continuous strict partial order
zbMATH Keywords: topology of closed convergence
MaRDI profile type: Publication
full work available at URL: 0165-4896(88)90021-2
OpenAlex ID: W2034921478
cites work: Q4070950
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description: scientific article; zbMATH DE number 4045438