函数一致连续与连续的关系讨论

Examples of the Relationship between Uniformly Continuous Function and Continuous Function

函数f(x)在区间I上一致连续,可得f(x)在区间I上连续,反之不一定.若I为有限闭区间[a,b],据Cantor定理,f(X)在[a,b]上连续等价于f(X)在[a,b]上一致连续.通过几个具体例题的证明,探讨了开区间以及无穷区间上一致连续与连续的关系.

f（x） uniformly continuous function in the interval I is made available in the intervalon the straight and vice versa is not necessarily. If I is limited closed interval [ a, b], according to Cantor theorem, continuous[ a, b] is equivalent to - uniformly fx . From the evidence of a number of specific examples, this article discusses the relationship between uniforinly continuation and continuation in the open interval and the infinite interval.