التفاصيل البيبلوغرافية
| العنوان: |
The Banach-Tarski paradox for some subsets of finite-dimensional normed spaces over non-Archimedean valued fields |
| المؤلفون: |
Orzechowski, Kamil |
| سنة النشر: |
2024 |
| المجموعة: |
Mathematics |
| مصطلحات موضوعية: |
Mathematics - Functional Analysis, Mathematics - Group Theory, Mathematics - Representation Theory, Primary 47S10, Secondary 46S10, 12J25, 26E30, 20E05, 20H20, 46B04, 05A18, 03E25 |
| الوصف: |
We show some results related to the classical Banach-Tarski paradox in the setting of finite-dimensional normed spaces over a non-Archimedean valued field $K$. For instance, all balls and spheres in $K^n$, and the whole space $K^n$ (for $n\ge 2$) are paradoxical with respect to certain groups of isometries of $K^n$. If $K$ is locally compact (e.g., $K$ is the field $\mathbb{Q}_p$ of $p$-adic numbers for any prime number $p$), any two bounded subsets of $K^n$ with nonempty interiors are equidecomposable (and paradoxical) with respect to a certain group of isometries of $K^n$ (for $n\ge 2$). |
| نوع الوثيقة: |
Working Paper |
| URL الوصول: |
http://arxiv.org/abs/2402.14772 |
| رقم الانضمام: |
edsarx.2402.14772 |
| قاعدة البيانات: |
arXiv |