集上的连续函数及一致连续函数的延拓问题

The Continuation Problem of Continuous Function and Uniformly Continuous Function in Sets

已知函数在开区间内一致连续,可证得在处有有限极限(指单侧极限存在)。因此,如果将极限值分别作为在处的值,则可以被延拓到闭区间,且在上一致连续。同样,把连续及一致连续的概念推广到一般的集合上,也有类似的结论。

If f （x） is uniformly continuous function in the open interval （a, b）, the existence of limit of [ a, b ], and will be uniformly continuous in [ a, b ]. Similarly, if the concepts of continuity and uniform continuity were extended to a general set E belong to R , the same conclusion could be drawn.