Theorem of nested closed interval in R~1 is generalized to generic complete metric space. The theorem in R~n is its particular case. The theorem of accumulation point in R~n can proved by theorem of nested interval in R~n.

• 从两个方面对实数集R1上的闭区间套定理进行了推广；得到了一般完备度量空间上的闭区间套定理；而一般实数集Rn空间上的闭区间套定理为其特例；并利用Rn空间上的闭区间套定理得到了Rn空间上的聚点定理.