Kamil Orzechowski

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20242026

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math.FA2026

The Banach-Tarski paradox in complete discretely valued fields

Kamil Orzechowski

We prove some results related to the classical Banach--Tarski paradox in the setting of a field $K$ that is complete with respect to a discrete non-Archimedean valuation (…

math.FA2025

Paradoxical decompositions of finite-dimensional non-Archimedean normed spaces

Kamil Orzechowski

We show that any normed space $(K^{n}, ∥ \cdot ∥)$ , $n \geq 2$ , over a field $K$ equipped with a nontrivial non-Archimedean valuation admits a paradoxical decomposition using four piece…

math.FA2024

The Banach-Tarski paradox for some subsets of finite-dimensional normed spaces over non-Archimedean valued fields

Kamil Orzechowski

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 ba…