REMARKS ON THE CONTINUITY OF FUNCTIONS OF TWO VARIABLES

被引：0

作者：

McAsey, Michael ^{[1
]}

Mou, Libin ^{[1
]}

机构：

[1] Bradley Univ, Dept Math, Peoria, IL 61625 USA

来源：

REAL ANALYSIS EXCHANGE | 2011年 / 37卷 / 01期

关键词：

continuity; two variables; collections of paths;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The continuity of f(x, y) at (x(0), y(0)) can be described by the behavior of f along a collection of paths toward (x(0), y(0)) if the collection is rich enough. The collection of paths that are C-1 and convex is rich enough but the collection of differentiable functions with bounded derivatives is not. The collection of C-n parameterized paths (x(t), y(t)) for any n > 0 is also rich enough to capture continuity.

引用

页码：167 / 176

页数：10