处处连续处处不可微多元函数集合的性质

Properties on the set of continuous nowhere differentiable functions with several variables

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.

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.