Upper Semicontinuous Extensions of Binary Relations

Walter Bossert, Yves Sprumont () and Kotaro Suzumura

Cahiers de recherche from Universite de Montreal, Departement de sciences economiques

Abstract: Suzumura shows that a binary relation has a weak order extension if and only if it is consistent. However, consistency is demonstrably not sufficient to extend an upper semi-continuous binary relation to an upper semicontinuous weak order. Jaffray proves that any asymmetric (or reflexive), transitive and upper semicontinuous binary relation has an upper semicontinuous strict (or weak) order extension. We provide sufficient conditions for existence of upper semicontinuous extensions of consistence rather than transitive relations. For asymmetric relations, consistency and upper semicontinuity suffice. For more general relations, we prove one theorem using a further consistency property and another with an additional continuity requirement.

Keywords: extensions; uer semicontinuity; consistency (search for similar items in EconPapers)
JEL-codes: C10 (search for similar items in EconPapers)
Pages: 16 pages
Date: 2002
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://hdl.handle.net/1866/369 (application/pdf)

Related works:
Journal Article: Upper semicontinuous extensions of binary relations (2002)
Working Paper: Upper Semicontinuous Extensions of Binary Relations (2002)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:mtl:montde:2002-01

Access Statistics for this paper

More papers in Cahiers de recherche from Universite de Montreal, Departement de sciences economiques Contact information at EDIRC.
Bibliographic data for series maintained by Sharon BREWER ().