| 序列连续性与拓扑连续性 |
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| 引用本文： | 张志尧.序列连续性与拓扑连续性[J].天津工业大学学报,2001,20(4):29-31,33. |
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| 作者姓名： | 张志尧 |
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| 作者单位： | 天津医科大学, |
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| 摘 要： | 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－LCL空间，文中证明了LCL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LCL空间的拓扑结构。
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| 关 键 词： | 序列收敛 拓扑向量空间 序列连续性 拓扑连续性 |
| 文章编号： | 1671-024(2001)04-0029-03 |
On sequential continuity and topological continuity |
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| ZHANG Zhi,yao.On sequential continuity and topological continuity[J].Journal of Tianjin Polytechnic University,2001,20(4):29-31,33. |
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| Authors: | ZHANG Zhi yao |
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| Abstract: | 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. |
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| Keywords: | sequential convergence topological vector space sequential continuity topological continuity |
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