6 papers
Star operation, microscopic sets and porous sets
Daria Perkowska, Szymon Żeberski
This paper explores the interplay between star operations, microscopic sets, and porous sets. The study focuses on the Galvin-Mycielski-Solovay theorem, which characterizes strongl…
An Ideal Zoo in the Baire Space
Łukasz Mazurkiewicz, Marcin Michalski, Szymon Żeberski
In this paper, we study the translations into the Baire space of several well-known -ideals and families originally defined on the Cantor space, using their combinatorial charac…
On algebraic sums, trees and ideals in the Baire space
Łukasz Mazurkiewicz, Marcin Michalski, Robert Rałowski +1
We work in the Baire space equipped with the coordinate-wise addition . Consider a ideal and a family of some kind of perfect trees…
Mycielski among trees
Marcin Michalski, Robert Rałowski, Szymon Żeberski
Two-dimensional version of the classical Mycielski theorem says that for every comeager or conull set there exists a perfect set such that $…
Nonmeasurable sets and unions with respect to selected ideals especially ideals defined by trees
Robert Ralowski, Szymon Zeberski
In this paper we consider nonmeasurablity with respect to sigma-ideals defined be trees. First classical example of such ideal is Marczewski ideal s_0. We will consider also ideal…
Nonstandard proofs of Eggleston like theorems
Szymon Zeberski
We prove theorems of the following form: if is a big set, then there exists a big set and a perfect set …