| 连续函数列的极限函数需要满足的充分条件和必要条件 |
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| 引用本文： | 郑利凯.连续函数列的极限函数需要满足的充分条件和必要条件[J].河北北方学院学报(自然科学版),2011,27(2):1-3,7. |
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| 作者姓名： | 郑利凯 |
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| 作者单位： | 内蒙古民族大学数学学院,内蒙,古通辽,028000 |
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| 基金项目： | 内蒙古自治区自然基金资助项目 |
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| 摘 要： | 研究Rn上的函数f是Rn上一列连续函数{nfn}的极限函数的必要条件和充分条件.利用Baire定理,给出了连续函数列的极限函数必须满足的必要条件.通过构造连续函数列逼近已知函数,给出了连续函数列的极限函数必须满足的充分条件.
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| 关 键 词： | 极限函数 连续函数 Rn 必要条件 充分条件 Baire定理 |
Sufficient Condition and Necessary Condition for the Limiting Function of a Sequence of Continuous Functions |
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| ZHENG Li-kai.Sufficient Condition and Necessary Condition for the Limiting Function of a Sequence of Continuous Functions[J].Journa of Hebei North University:Natural Science Edition,2011,27(2):1-3,7. |
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| Authors: | ZHENG Li-kai |
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| Institution: | ZHENG Li-kai(College of Mathematics,Inner Mongolia University for the Nationalities,Tongliao 028000,Inner Mongolia,China) |
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| Abstract: | The paper studies the necessary condition and sufficient condition for function f on Rn being the limiting function of a sequence of continuous functions {fn}.On the basis of Baire theory,a necessary condition for a function on Rn being the limiting function of a sequence of continuous functions has been found.By constructing a sequence of continuous functions to approximate a known function,the paper gives a sufficient condition for a function on Rn being the limiting function of a sequence of continuous f... |
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| Keywords: | limiting function continuous function Rn necessary condition sufficient condition Baire theory |
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