A KKM-result and an application for binary and non-binary choice functions
type: Item
instance of: scholarly article
title: A KKM-result and an application for binary and non-binary choice functions
zbMATH Open document ID: 1035.91022
author: M. Carmen Sánchez
author: Juan-Vicente Llinares
author: Begoña Subiza
published in: Economic Theory
publication date: 2003-03-25T00:00:00Z
review text: The KKM theorem gives a sufficient condition for the intersection of a finite family of closed subsets of \(\mathbb R^n\) to be non-empty. The authors generalize this result to subsets of a class of topological spaces, called \(L\)-spaces. A generalized KKM-correspondence from a topological space \(Y\) to an \(L\)-space \(X\) is one that respects the \(L\)-structure on \(X\). Theorem 1 provides the generalization of the KKM theorem to this context. The authors then apply the result to obtain a condition on the existence of maximal elements for binary choice functions and a non-emptiness condition for non-binary choice functions.
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 91B06
Mathematics Subject Classification ID: 91B08
zbMATH DE Number: 1887535
zbMATH Keywords: KKM theorem
zbMATH Keywords: non-empty choice
zbMATH Keywords: non-binary choice function
zbMATH Keywords: maximal elements
zbMATH Keywords: tournaments
reviewed by: Duncan J. Melville
MaRDI profile type: Publication
full work available at URL: s00199-001-0242-y
OpenAlex ID: W1486524867
DOI: 10.1007/S00199-001-0242-Y
description: scientific article; zbMATH DE number 1887535