摘要
有界函数空间B(I)中的点态收敛不具备完备性 .B(I)中的均匀收敛拓扑具有 3条特征性质 ,强于点态收敛的完备范数拓扑只有均匀收敛拓扑 .Arzela给出的连续函数列极限函数连续的充要条件 ,其中拓扑不可能是范数拓扑 .
Pointwise convergence has no completeness in bounded function space B(I). The topology of uniform convergence has three characteristic properties in B(I). A complete norm topology stronger than the topology of poingwise convergence can only be one of uniform convergences. Arzela gave a necessary and sufficient condition of continuation of limit functions in sequences of continuous functions, among which topology can not be a norm topology.
出处
《邵阳学院学报（自然科学版）》
2004年第1期1-1,25,共2页
Journal of Shaoyang University：Natural Science Edition
基金
湖南省教育厅科研基金项目
关键词
点态收敛
均匀收敛
赋值映射
弱拓扑
闭算子
闭图象定理
拓扑同胚
B(I)空间
pointwise convergence
uniform convergence
evaluation mapping
weak toplolgy
closed operator
closed graph theorem
topological homomorphism
