Lexicographic behaviour of chains
type: Item
instance of: scholarly article
title: Lexicographic behaviour of chains
zbMATH Open document ID: 0924.06001
author: Esteban Induraín
author: Juan C. Candeal
published in: Archiv der Mathematik
publication date: 1999-06-30T00:00:00Z
review text: The problem of representability of ordered sets by means of real-valued order-preserving functions is very natural in the theory of ordered sets and is important for applications. It is known that a chain is representable if and only if it is perfectly separable. The authors of the paper study more general cases of numerical representations of chains. They prove among others that any countably bounded connected chain \(Z\) admits a lexicographic decomposition as a subset of the lexicographic product \(\mathbb{R}\times Z\). Both necessary and sufficient conditions for the lack of utility functions are also discussed there.
Mathematics Subject Classification ID: 06A05
Mathematics Subject Classification ID: 91B16
zbMATH DE Number: 1295485
zbMATH Keywords: planar chain
zbMATH Keywords: numerical representations of chains
zbMATH Keywords: lexicographic decomposition
zbMATH Keywords: lexicographic product
zbMATH Keywords: utility functions
reviewed by: Jiří Rachůnek
MaRDI profile type: Publication
full work available at URL: s000130050315
OpenAlex ID: W2066211746
DOI: 10.1007/S000130050315
description: scientific article; zbMATH DE number 1295485