一类二元函数连续性的等价刻画及在三角模上的应用  

An Equivalent Statement on the Continuity of a Classof Two Variables Functions and Its Application on Triangular Norms

作　　者：张德利[1] 郭彩梅[2] 

机构地区：[1]吉林省教育学院,吉林长春130022 [2]长春大学基础科学系,吉林长春130022

出　　处：《模糊系统与数学》2007年第4期6-8,共3页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(10271035)

摘　　要：关于二元函数的连续,经典数学分析中有熟知的结果,即"如果二元函数连续,则必关于每个单变量连续。反之,则未必"。本文证明对于单调且对称的二元函数而言,其二元连续等价于单变量连续,并重新定义了三角模的连续。As to the continuity of a two variables function, there exists the familiar result in the classical analysis, i.e. A two variables function is continuous on each variable if it is continuous, and the contrary is not correct. The present paper proves that： For a monotone and commutative two variables function, its continuity is equivalent to the continuity on each variable, and the continuity of triangular. Norms is redefined.

关 键 词：二元函数 连续 三角模 

分 类 号：O172[理学—数学]