Michał Dybowski

collaborators

3 papers

math.CA2026

Lebesgue Covering Theorem and level sets of continuous functions

MichaÅ Dybowski

We formulate and prove a dimension-theoretic generalization of a version of the Lebesgue Covering Theorem. A generalized $n$ -dimensional version of the Steinhaus Chessboard Theorem…

math.GN2026

Chessboard and level sets of continuous functions

MichaÅ Dybowski, Michał Dybowski, PrzemysÅaw GÃ³rka +1

We provide the following result and its discrete equivalent: Let $f : I^{n} \to R^{n - 1}$ be a continuous function. Then, there exist a point $p \in R^{n - 1}$ an…

math.LO2024

Maximal Î´-separated sets in separable metric spaces and weak forms of choice

MichaÅ Dybowski, Przemyslaw GÃ³rka, Paul Howard

We show that the statement ``In every separable pseudometric space there is a maximal non-strictly Î´-separated set.'' implies the axiom of choice for countable families of sets. T…