Výsledky vyhledávání - "Dybowski, Michal P."

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Chessboard and level sets of continuous functions

Autor: Dybowski, Michał, Górka, Przemysław

We provide the following result and its discrete equivalent: Let $f \colon I^n \to \mathbb{R}^{n-1}$ be a continuous function. Then, there exist a point $p \in \mathbb{R}^{n-1}$ and a compact subset $S \subset f^{-1}\left[\left\{p\right\}\right]$ whi

Externí odkaz: http://arxiv.org/abs/2406.13774

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Maximal \delta-separated sets in separable metric spaces and weak forms of choice

Autor: Dybowski, Michał, Górka, Przemyslaw, Howard, Paul

We show that the statement ``In every separable pseudometric space there is a maximal non-strictly \delta-separated set.'' implies the axiom of choice for countable families of sets. This gives answers to a question of Dybowski and G\'{o}rka in [M. D

Externí odkaz: http://arxiv.org/abs/2405.10466

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