| 拓扑空间中函数上（下）极限的一些性质 |
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| 引用本文： | 卢天秀,朱培勇,辛邦颖. 拓扑空间中函数上（下）极限的一些性质[J]. 四川轻化工学院学报, 2011, 0(3): 264-266 |
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| 作者姓名： | 卢天秀 朱培勇 辛邦颖 |
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| 作者单位： | [1]四川理工学院理学院,四川自贡643000 [2]电子科技大学数学科学学院,成都611731 [3]西昌学院汽车与电子工程学院,四川西昌615013 |
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| 基金项目： | 国家自然科学基金资助项目（10671134）; 四川理工学院科研基金（2009XJKYL007） |
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| 摘 要： | 结合拓扑空间的特性讨论函数上（下）极限,得到了一些与实直线上几乎一致的结果。首先给出了拓扑空间中函数上（下）极限的定义。然后证明了满足第一可数性公理的拓扑空间中函数上（下）极限是子极限集的最大（小）元。针对在某点存在单调递减的可数邻域基的函数,得到了上（下）极限的等价条件和几个性质。
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| 关 键 词： | 拓扑空间 上（下）极限 第一可数 |
Some Properities of Upper and Lower Limits of a Function on Topological Space |
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| LU Tian-xiu,ZHU Pei-yong,XIN Bang-ying. Some Properities of Upper and Lower Limits of a Function on Topological Space[J]. Journal of Sichuan Institute of Light Industry and Chemical Technology, 2011, 0(3): 264-266 |
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| Authors: | LU Tian-xiu ZHU Pei-yong XIN Bang-ying |
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| Affiliation: | 1.School of Science,Sichuan University of Science ＆ Engineering,Zigong 643000,China;2.School of Mathematical Science,University of Electronic Science and Technology of China,Chengdu 611731,China;3.School of Automotive and Electronic Engineering,Xichang College,Xichang 615013,China) |
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| Abstract: | Combined with properities of topological space,this paper discussed the upper and lower limits of a function,obtained some results which relatively similar to the ones on real line.First,the concept of upper and lower limits of a function in topological space is defined.Then it is proved that upper and lower limits of a function on first-countable topological space is the largest（smallest） element of sub-limit set.Also,the equivalent conditions and some properities of the function with monotone decreasing countable neighborhood basis at a point are obtained. |
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| Keywords: | topological space upper and lower limits first-countable |
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