7 papers
More on dominated and microscopic sets
Ondřej Zindulka, Piotr Nowakowski, Cristina Villanueva-Segovia
Let be a family of sequences decreasing to zero. A set in a metric space is -dominated if, for every , there exists a countable cover of such that…
A characterization of uniqueness of purely atomic finite measures with central Cantor set range
Piotr Nowakowski, Franciszek Prus-Wiśniowski
We study purely atomic measures whose range is a central Cantor set and characterize those central Cantor sets that are the range of exactly one such measure. Next, we extend the c…
Dominated sets, microscopic sets and Hausdorff measures
Ondřej Zindulka, Piotr Nowakowski
Let be a family of sequences of positive numbers that decrease to 0, let be a metric space and . is said to be -dominated if, for every , a coun…
Spectre operator, achievement sets and sets of P-sums in a hyperspace of compact sets
Piotr Nowakowski, Franciszek Prus-Wiśniowski, Filip Turoboś
Let be an Abelian metric group and . We investigate the spectre of a set , defined as the set of all elements such that for every either…
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…
The algebraic difference of a Cantor set and its complement
Piotr Nowakowski, Cheng-Han Pan
Let be a Cantor set. In the classical problems, modifying the ``size'' of has a magnified effect on $\mathcal{…
Algebraic sums of achievable sets involving Cantorvals
Jacek Marchwicki, Piotr Nowakowski, Franciszek Prus-Wiśniowski
In this paper we look at the topological type of algebraic sum of achievement sets. We show that there is a Cantorval such that the algebraic sum of its copies is still a Canto…