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| 拓扑空间中函数上(下)极限的一些性质 | |
| 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].四川理工学院学报(自然科学版),2011,24(3):264-266. |
| 作者姓名： | 卢天秀 朱培勇 辛邦颖 |
| 作者单位： | 1. 四川理工学院理学院,四川自贡643000;电子科技大学数学科学学院,成都611731 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 |
| 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) |
| 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。 |
| 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-ring.Some Properities of Upper and Lower Limits of a Function on Topological Space[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,2011,24(3):264-266. | |
| Authors: | LU Tian-xiu ZHU Pei-yong XIN Bang-ring |
| Institution: | LU Tian-xiu,ZHU Pei-yong,XIN Bang-ying(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 611731,3.School of Automotive and Electronic Engineering,Xichang College,Xichang 615013,China) |
| 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 c... |
| Keywords: | topological space upper and lower limits first-countable |
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