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arXiv · 2108.00812

Isometries of ultrametric normed spaces

Javier Cabello Sánchez·José Navarro Garmendia
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Abstract

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 Probl\`eme 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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Javier Cabello Sánchez, José Navarro Garmendia. 2021-08-02. Isometries of ultrametric normed spaces. https://arxiv.org/abs/2108.00812

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