Year: 2025
Type: article
Abstract: We show that any normed space $(K^n,\lVert\cdot\rVert)$, $n\ge 2$, over a field $K$ equipped with a nontrivial non-Archimedean valuation admits a paradoxical decomposition using four pieces with respect to the group of its affine isometries, provided that the norm $\lVert\cdot\rVert$ is equivalent to the maximum norm. It follows that any finite-dimensional normed space $(X,\lVert\cdot\rVert)$ with dim${X}\ge 2$ over a complete non-Archimedean nontrivially valued field $(K,\lvert\cdot\rvert)$ is paradoxical using four pieces with respect to the group of its affine isometries.
Author: Kamil Orzechowski
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4413836382