半连续函数空间的若干性质

Some properties of semi-continuous function space

首先引入上半一致收敛的概念.然后利用上半一致收敛定义了半连续函数集上的闭包运算,同时赋予了半连续函数集在此运算下的拓扑.最后得出了此空间为T3空间.

This paper first introduces the notion of semi-uniform convergence, and then uses this notion to define the formulation of closure which is defined on the set of all semi-continuous function. Meanwhile, the topology of the set mentioned above is given by means of closure formulation. Finally, it is proved that this topological space is T3.