序列连续性与拓扑连续性(英文)

On sequential continuity and topological continuity

首先在线性空间中给出一个序列收敛关系 ,然后利用列邻域得到了由绝对凸吸收集构成的可加滤子基 ,进而构成了局部凸空间—— L CL空间 ,文中证明了 L CL空间的重要特征是序列连续性等价于拓扑连续性 ,并讨论了 L CL空间的拓扑结构 .

In this paper,a sequential convergence in vector space is first given,then,from the sequential neighborhoods,the additive filterbase of absolutely convex absorbing sets is obtained,a local convex topological vector space,LCL space,is constructed.The important characteristic of the LCL space is that sequential continuity is equivalent to topological continuity.Also,the structure of topology of LCL space is discussed.