| 处处连续处处不可微多元函数集合的性质 |
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| 引用本文： | 谈强,徐海峰.处处连续处处不可微多元函数集合的性质[J].扬州大学学报(自然科学版),2011(4). |
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| 作者姓名： | 谈强 徐海峰 |
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| 作者单位： | 扬州大学数学科学学院; |
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| 基金项目： | 国家自然科学基金资助项目(11071208,11101352,11126046) |
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| 摘 要： | 证明了C(0,1]n)中处处不可微函数集合的补集是第一纲集.证明思路沿用n=1时的情形,但通过构造一系列疏集,使证明中不等式的得出更为自然.通过对证明的详细分析,可以得到向量值连续函数空间也有类似的性质.最后讨论了协变导数代替偏导数的情形.
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| 关 键 词： | 多元函数 奇点稠密原理 有界线性算子 第一纲集 协变微分 |
Properties on the set of continuous nowhere differentiable functions with several variables |
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| TAN Qiang,XU Hai-feng.Properties on the set of continuous nowhere differentiable functions with several variables[J].Journal of Yangzhou University(Natural Science Edition),2011(4). |
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| Authors: | TAN Qiang XU Hai-feng |
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| Institution: | TAN Qiang,XU Hai-feng* (Sch of Math Sci,Yangzhou Univ,Yangzhou 225002,China) |
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| Abstract: | It is proved that the complement of the set of nowhere differentiable functions in C(n) is a first category set by the similar way in the case of n=1.The author improves the definition of the constructed nowhere dense sets so that one of useful inequalities is naturally inferred out.By analysis of the original proof,it is found that the space of vector valued continuous functions has similar properties.And the result for the covariant derivative of Rn is also generalized. |
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| Keywords: | multi-function singularity dense theory bounded linear operator first category set covariant derivative |
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