essential superior limit

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.

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。

According to the definition of upper limit and lower limit of function on a certain spot in the distance space,and the definition of upper continuity and lower continuity of function on a certain spot,the article proves the equivalence condition of the upper continuity of function on a certain spot.

根据距离空间中函数在某点的上极限、下极限的定义及函数在某点上半连续、下半连续的定义,证明了函数在某点上半连续的等价条件。

Discuss the commutative problem of a continuous and monotonically function with upper limit,and obtains a good method for counting the upper limit.

探讨了连续单调函数与上极限运算交换的问题 ,从而为求上极限提供了一个有力工

In this paper,we introduced the cone topology concept,then defined cone limit point,cone cluster point of net and set net,and then defined cone upper limit,cone lower limit,cone limit of set net,the last we proved several properties for it.

引入拓扑线性空间中的锥拓扑概念,并由此定义了网和集网的锥极限点、锥聚点和集网的锥上极限、锥下极限、锥极限,给出并证明了集网的锥上极限、锥下极限、锥极限的一些性质。

The properties of weak colimits are discussed systematically.

系统讨论了弱上极限与弱极限的有关性质 ,并且利用弱上极限的语言给出了Brown表示定理的一个新的表