Piotr Nowakowski

activity

20232026

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Showing 2025Show all

3 papers · 1 filter

math.GN2025

Spectre operator, achievement sets and sets of P-sums in a hyperspace of compact sets

Piotr Nowakowski, Franciszek Prus-Wiśniowski, Filip Turoboś

Let $(X, +, d)$ be an Abelian metric group and $A \subset X$ . We investigate the spectre of a set $A$ , defined as the set of all elements $z \in X$ such that for every $x \in A$ either…

math.DS2025

The Lebesgue measure of boundaries of multigeometric Cantorvals

Piotr Nowakowski, Franciszek Prus-Wiśniowski

We prove that the boundary of every multigeometric Cantorval is a null set, and extend this result to a larger class of standard achievable Cantorvals. In addition, we discuss the…

math.CA2025

The algebraic difference of a Cantor set and its complement

Piotr Nowakowski, Cheng-Han Pan

Let $C \subseteq [0, 1]$ be a Cantor set. In the classical $C \pm C$ problems, modifying the ``size'' of $C$ has a magnified effect on $\mathcal{…