Some topological minimax theorems
type: Item
instance of: scholarly article
title: Some topological minimax theorems
zbMATH Open document ID: 0980.49006
DOI: 10.1007/BF02675799
author: B. R. Frenkin
published in: Mathematical Notes
publication date: 2002-02-19T00:00:00Z
review text: Let \(X, Y\) be topological spaces and \(F(x,y)\) be defined on \(X \times Y\). The minimax theorems establish conditions under which \[ \inf_{y \in Y} \sup_{x \in X}F(x,y)= \sup_{x \in X} \inf_{y \in Y}F(x,y). \] Two such theorems are proved with no restrictions on \(X,Y\) except for those related to the function \(F(x,y)\). The conditions concerning the behavior of the function deal only with the interval between the minimax and maximin. The scheme of arguments goes back to the Hahn-Banach theorem and the separating hyperplane theorem.
Mathematics Subject Classification ID: 49J35
zbMATH DE Number: 1517728
zbMATH Keywords: topological spaces
zbMATH Keywords: minimax theorems
reviewed by: Mikhail Yu. Kokurin
MaRDI profile type: Publication
cites work: Q5724368
cites work: On general minimax theorems
cites work: Convex Analysis
cites work: Theory of games and economic behavior.
description: scientific article; zbMATH DE number 1517728