非对称度量空间中的上收敛性

On Convergence in the Quasi-metric Spaces

研究非对称度量空间的收敛性。提出了非对称度量空间的上、下极限概念,解决了非对称度量空间上收敛性的基本问题,得出了上极限,下极限,子序列极限之间的关系及上闭集、上柯西序列、上完备集的有关结果,证明了Hausdorff半距离空间是上完备的非对称度量空间。

This paper investigates the problem of convergence in the quasi-metric space.For this purpose,new concepts in the quasi-metric space are proposed including the upper limit,upper closed set,upper Cauchy sequence and upper completeness,and some important results about the concepts have been obtained.It is shown that Hausdorff semidistance space is an upper completeness quasi-metric space.