二元函数连续性与沿曲线的连续性之间的关系  

Continuity of Binary Functions and Continuity along Curves

作　　者：刘雪 常建明[1] LIU Xue;CHANG Jianming(School of Mathematics and Statistics,Changshu Institute of Technology,Changshu 215500,China)

机构地区：[1]常熟理工学院数学与统计学院,江苏常熟215500

出　　处：《常熟理工学院学报》2022年第2期116-119,共4页Journal of Changshu Institute of Technology

摘　　要：平面区域内的连续函数沿该区域内的任何连续曲线自然是连续的,但反之未必.本文证明:如果平面区域内的一个函数沿覆盖该区域的两相交可求长连续曲线族是连续的,并且沿其中一族曲线具有单调性,则该函数在该区域连续.A continuous function in a domain is naturally continuous along every continuous curve contained in the domain,but the inverse is generally untrue.We prove that if a function in a domain is continuous along two intersecting families of continuous curves covering the domain and has monotonicity along the curves in one family,then the function is continuous in the domain.

关 键 词：二元函数 连续性 连续曲线族 单调性 

分 类 号：O174.1[理学—数学]