تقرير
On the concept of non-ultrametric non-Archimedean analysis
| العنوان: | On the concept of non-ultrametric non-Archimedean analysis |
|---|---|
| المؤلفون: | Sánchez, Javier Cabello, Fuertes, Francisco J. Carmona |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, 26E30, 11E95 |
| الوصف: | Given some non-Archimedean field $\mathbb{K}$ and some $\mathbb{K}$-linear space $X$, the usual way to define a norm over $X$ involves the {\em ultrametric inequality} $\|x+y\|\leq\max\{\|x\|,\|y\|\}$. In this note we will try to analyse the convenience of considering a wider variety of norms. The main result of the present note is a characterisation of the isometries between finite-dimensional linear spaces over some valued field endowed with the norm $\|\,\cdot\,\|_1$, a result that can be seen as the closest to a Mazur--Ulam Theorem in non-Archimedean analysis. Comment: 8 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2108.12400 |
| رقم الأكسشن: | edsarx.2108.12400 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |