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。
A new theorem on upper-lower limit is given in this paper.
给出了关于上、下极限的一个新定理,并举例说明了该定理的应用。
With the making use of lower limit and upper limit,the intermediate value theorem is generalized to general discontinuous function.
研究了非连续函数的介值定理,受朱乐敏等考虑的具有左、右极限存在的跳跃间断点的非连续函数的介值性定理的启发,利用上、下极限把介值定理推广到具有一般间断点的非连续函数的情况。
L Hopital laws on upper limit and lower limit are being introduced.
指出前一集合含于后一集合,导出了上、下极限形式的罗必塔(L'Hospital)法则,阐明了罗必塔法则适用和失效的根本原因。