Comparison of some notions of Ck-maps in multi-variable non-archimedian analysis
Comparison of some notions of Ck-maps in multi-variable non-archimedian analysis
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多变量非阿基米德分析中 Ck-map 的一些概念比较
DOI：
10.36045/bbms/1197908901
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发表时间：
2006
影响因子：
0.5
通讯作者：
Helge Glöckner
中科院分区：
文献类型：
--
作者：
Helge Glöckner
在文献中已经提出了有限维向量空间开子集上C^k映射的各种定义。我们证明了Schikhof和De Smedt所考虑的C^k图与Bertram， Glockner和Neeb的C^k图是一致的。相比之下，Ludkovsky的C^k映射在前一种意义上不必是C^k，至少在正特征上是这样。我们还比较了有限维空间和可度量空间上的各种类型的Holder可微映射。
Various definitions of C^k-maps on open subsets of finite-dimensional vector spaces over a complete valued field have been proposed in the literature. We show that the C^k-maps considered by Schikhof and De Smedt coincide with those of Bertram, Glockner and Neeb. By contrast, Ludkovsky's C^k-maps need not be C^k in the former sense, at least in positive characteristic. We also compare various types of Holder differentiable maps on finite-dimensional and metrizable spaces.