B(I)空间中两种收敛的拓扑比较  

A Comparison between Topologies of Two Classes of Convergence in B(I) Space

作　　者：李经文[1] 

机构地区：[1]邵阳学院数学系,湖南邵阳422000

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

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.

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 

分 类 号：O177.2[理学—数学]