Numerical representability of ordered topological spaces with compatible algebraic structure
type: Item
instance of: scholarly article
title: Numerical representability of ordered topological spaces with compatible algebraic structure
zbMATH Open document ID: 1241.54020
author: Esteban Induraín
author: José A. Molina
author: Juan C. Candeal
published in: Order
publication date: 2012-03-23T00:00:00Z
review text: This paper is devoted to the study of continuous numerical representations of totally preordered topological vector spaces through real-valued order-preserving functions that are also algebraic homomorphisms. The main novelty is the analysis of numerical representations that are continuous, linear and multiplicative, motivated from applications in Economics and Social Sciences. For this the authors endow totally preordered topological vector spaces with an additional binary relation, compatible with the given preorder, obtaining the category of totally preordered semitopological real algebras. They provide conditions that characterize the existence of continuous real-valued order-preserving maps that are linear and multiplicative and represent total preorders defined on a semitopological real algebra. Then they present a number of results inspired by important concepts and issues arising in Economics, Social Choice and Decision-Making theories (like the problem of aggregating individual judgements or opinions into a social one). There is a flaw in Theorem 3.14 due to a condition missing in Definition 3.5. This has recently been corrected by the authors in an erratum [Order 29, No. 1, 227--227 (2012; Zbl 1236.54029)].
reviewed by: Jorge Picado
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 06F25
Mathematics Subject Classification ID: 91B14
zbMATH DE Number: 6018075
zbMATH Keywords: totally preordered topological spaces
zbMATH Keywords: continuous numerical representations of total preorders
zbMATH Keywords: totally preordered algebraic structures
zbMATH Keywords: semitopological real algebras
zbMATH Keywords: social choice theory
MaRDI profile type: Publication
full work available at URL: s11083-011-9202-8
OpenAlex ID: W2059594485
cites work: Q4267848
cites work: Social choice and individual values
cites work: Utility Theory without the Completeness Axiom
cites work: Q3979160
cites work: Q5532570
cites work: Q3927416
cites work: A note on the existence of continuous representations of homothetic preferences on a topological vector space
cites work: Continuous representability of homothetic preferences by means of homogeneous utility functions
cites work: Numerical representations of interval orders
cites work: Unified representability of total preorders and interval orders through a single function: the lattice approach
cites work: Continuous representability of homothetic preorders by means of sublinear order-preserving functions
cites work: Representations of preference orderings
cites work: Q3595917
cites work: Order embeddings with irrational codomain: Debreu properties of real subsets
cites work: Topological additively representable semigroups
cites work: Q4938540
cites work: On the structure of homothetic functions
cites work: Q4299052
cites work: Homothetic and weakly homothetic preferences
cites work: Order preserving functions on ordered topological vector spaces
cites work: Utility Functions on Partially Ordered Topological Groups
cites work: A note on linear utility
cites work: Ordered Topological Spaces
cites work: On preference relations which satisfy weak independence property
cites work: On scaling laws for production functions
cites work: Q3962738
cites work: Q5509706
cites work: Equity in Two Person Situations: Some Consequences
cites work: Q4044675
cites work: Existence of a utility in infinite dimensional partially ordered spaces
cites work: Stationary Ordinal Utility and Impatience
cites work: Q5639713
cites work: Q3993509
cites work: Continuous linear representability of binary relations
cites work: Topologically orderable groups
cites work: Q3272732
cites work: Q5613420
cites work: Q5635232
cites work: Q5325801
DOI: 10.1007/S11083-011-9202-8
Recommended article: Order representability in groups and vector spaces
Recommended article: Q5313943
Recommended article: The Continuous Representation Property in Utility Theory
Recommended article: Expected utility from additive utility on semigroups
Recommended article: Continuous order representability properties of topological spaces and algebraic structures
Recommended article: On continuous multi-utility representations of semi-closed and closed preorders
Recommended article: A note on linear utility
Recommended article: Order preserving functions on ordered topological vector spaces
Recommended article: Preorderable topologies and order-representability of topological spaces
Recommended article: Continuity and Continuous Multi-utility Representations of Nontotal Preorders: Some Considerations Concerning Restrictiveness
description: scientific article; zbMATH DE number 6018075