一致连续映射的两个扩张定理  

The Theorems of Extension of Uniformly Continuous Mapping

作　　者：张广计[1] 

机构地区：[1]西北政法大学经管学院,陕西西安710063

出　　处：《大学数学》2013年第2期56-58,共3页College Mathematics

摘　　要：把文[1],[2]中的两个定理进行了拓广和改进,给出两个一致连续映射的扩张定理:(i)任一集合A到一个完备度量空间的一致连续映射可一致连续扩张到A珡上.(ii)任一闭集A到Rn的一致连续映射可一致连续扩张到A与任一紧集的并.Abstract： Two theorems of the paper [1] and [2] are spread continuous mapping and uniformly continuous mapping are given： （i） a complete metric space can be uniformly continuously extended ton. set A into R^n can be uniformly continuously extended to the union of and improved, and two theorems of extension of A uniformly continuous mapping from a set A into （ii） A uniformly continuous mapping from a closed set A and any compact set.

关 键 词：一致连续映射 映射的扩张 紧集 Tietze扩张定理 

分 类 号：O172.2[理学—数学]