函数连续的连续扩张  

Continuously continuous extention of functions

作　　者：张丽丽[1,2] 范玲玲[3] 

机构地区：[1]西安工业学院数理系 [2]陕西西安710049 [3]汕头大学数学系

出　　处：《纺织高校基础科学学报》2004年第4期314-316,325,共4页Basic Sciences Journal of Textile Universities

摘　　要：用 (L ,‖ .‖ )表示赋范线性空间 ,用 (X,d)表示度量空间 ,A为 X的闭子集 ;用 C(X,L )表示从 X到 L的所有连续函数的全体 ,用 Cp(C,L ) ,Cco(X ,L )和 Cu(X ,L )分别表示C(X,L )带有点态收敛拓扑、紧开拓扑和一致收敛拓扑的函数空间 .证明了 映射 h:C(A,L )→ C(X,L ) ,使得 f∈ C(A,L ) ,h(f )为 f在 X上的一个连续扩张 ,且当 C(A,L ) ,C(X,L )分别被赋予了点态收敛拓扑、紧开拓扑和一致收敛拓扑时 。Let (L,‖·‖) be a normed linearly space.Let A be a closed subset of a metric space (X,d). C(X,L) is used to denote the family of all continuous maps from X to L.It is showed that there exists a map h:C(A,L)→C(X,L) such that for every f∈C(A,L),h(f) is a continuous extension over X,moreover,when C(A,L),C(X,L) are endowed with the topology of uniform convergence(resp,the topology of (pointwise) (convergence),compact-open topology),h is always continuous.

关 键 词：连续扩张 点态收敛 一致收敛 紧开拓扑 

分 类 号：O189.11[理学—数学]