Graphical convergence of continuous functions

被引：0
作者：
Gerald Beer
Somashekhar Naimpally
机构：
[1] California State University Los Angeles,Department of Mathematics
来源：
Acta Mathematica Hungarica | 2013年 / 140卷
关键词：
graph topology; continuous function; function space; distance functional; Hausdorff distance; Wijsman convergence; finite topology; locally finite topology; Vietoris topology; 54C35; 40A30; 54B20; 54C05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let X and Y be metrizable spaces. We show that convergence of a net of continuous functions 〈fλ〉 to a continuous function f in the graph topology for C(X,Y) is equivalent to the uniform convergence of the net of associated distance functionals for the graphs with respect to each compatible metric on X×Y. Remarkably, no weaker convergence results if uniform convergence is replaced by pointwise convergence in the last statement.
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页码：305 / 315
页数：10
相关论文
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