拓扑空间上半连续函数的等价条件

Some Equivalent Conditions of Semi-coutinuous Functions on Topological Space

首先给出了拓扑空间上网的上(下)极限和函数的上(下)极限的定义,以及一般拓扑空间到线性序拓扑空间的半连续函数的定义,然后得到了拓扑空间上函数连续和函数半连续的关系,最后证明了拓扑空间上函数半连续的几个等价条件.

In this paper,definitions of upper and lower limits for net and the one for function on topological space are given first,and the definition of semi-coutinuous function from topological space to ordered linear ordered topological space is given.Then,the relationship between coutinuous function and semi-coutinuous function on topological space is obtained.At last,some equivalent conditions of semi-coutinuous function on topological space is proved.