超度量赋范空间的等距
Isometries of ultrametric normed spaces
摘要：
我们证明了超度量赋范空间的等距群可以看作是一种分形。然后，我们应用这个描述来研究阿基米德分析中一些经典问题的超度量对应问题，如所谓的Problème des rotations de Mazur或Tingley问题。特别是，与实赋范空间的情况相反，超度量赋范空间之间的等距可以非常远离线性。
英文摘要：
We show that the group of isometries of an ultrametric normed space can be seen as a kind of a fractal. Then, we apply this description to study ultrametric counterparts of some classical problems in Archimedean analysis, such as the so called Problème des rotations de Mazur or Tingley's problem. In particular, it turns out that, in contrast with the case of real normed spaces, isometries between ultrametric normed spaces can be very far from being linear.
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