Further remarks on totally ordered representable subsets of Euclidean space

Candeal J.C., Indurain E. and Mehta G.B. (1996) Further remarks on totally ordered representable subsets of Euclidean space. Journal of Mathematical Economics, 25 4: 381-390. doi:10.1016/0304-4068(95)00734-2


Author Candeal J.C.
Indurain E.
Mehta G.B.
Title Further remarks on totally ordered representable subsets of Euclidean space
Journal name Journal of Mathematical Economics   Check publisher's open access policy
ISSN 0304-4068
Publication date 1996-01-01
Sub-type Article (original research)
DOI 10.1016/0304-4068(95)00734-2
Open Access Status Not yet assessed
Volume 25
Issue 4
Start page 381
End page 390
Total pages 10
Publisher Elsevier
Language eng
Subject 2002 Economics and Econometrics
2604 Applied Mathematics
Abstract We introduce the property of ≲ -norm-boundedness on totally ordered subsets of Euclidean spaces. We show that when a closed subset X of the Euclidean space ℝ, endowed with a continuous total order ≲, is ≲ -norm-bounded, the order topology and the induced Euclidean topology must coincide on X. This generalizes a recent result by Beardon, proved on connected totally ordered subsets of Euclidean space, because on totally ordered closed subsets of ℝ connectedness is a particular case of ≲ -norm-boundedness. We also analyze necessary and sufficient conditions for the coincidence of both topologies, and discuss some extension to the infinite-dimensional context.
Keyword Euclidean space
Normed spacesi
Ordered sets and order topologies
Topological vector spaces
Utility functions
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import - Archived
 
Versions
Version Filter Type
Citation counts: Scopus Citation Count Cited 4 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Tue, 22 Aug 2017, 00:13:21 EST by System User