4 citations · 10 across the 24 of their papers we have counts for
25 papers
Everywhere sets
Jakub Cieplechowicz, Szymon Żeberski
Let be a -ideal on the Cantor space . A set is called everywhere if for any the set $X\!\restriction\! S\in\mathca…
On Star operation and some ideals on the Baire space
Aleksander Cieślak, Daria Perkowska, Szymon Żeberski
We investigate several -ideals on the Baire space , introducing and studying the ideals and , alongside the classical ideals…
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…
On algebraic sums, trees and ideals in the Cantor space
Marcin Michalski, Robert Rałowski, Szymon Żeberski
We work in the Cantor space . The results of the paper adhere the following pattern. Let $\mathcal{I}\in \{\mathcal{M}, \mathcal{N}, \mathcal{M}\cap \mathcal{N}, \mathcal{E}\}…
Ideal Analytic sets
Łukasz Mazurkiewicz, Szymon Żeberski
The aim of this paper is to give natural examples of -complete and -complete sets. In the first part, we consider ideals on . In particular, we show…
Around Eggleston Theorem
Marcin Michalski, Robert Rałowski, Szymon Żeberski
The motivation of this work are the two classical theorems on inscribing rectangles and squares into large subsets of the plane, namely Eggleston Theorem and Mycielski Theorem. Usi…
Sequences with increasing subsequence
Łukasz Mazurkiewicz, Szymon Żeberski
We study analytic and Borel subsets defined similarily to the old example of analytic complete set given by Luzin. Luzin's example, which is essentially a subset of the Baire space…
Ideals with Smital properties
Marcin Michalski, Robert Rałowski, Szymon Żeberski
A -ideal on a Polish group has Smital Property if for every dense set and a Borel -positive set the algebraic sum is a complemen…
The Set-Cover game and nonmeasurable unions
Taras Banakh, Robert Rałowski, Szymon Żeberski
Using a game-theoretic approach we present a generalization of the classical result of Brzuchowski, Cichoń, Grzegorek and Ryll-Nardzewski on non-measurable unions. We also present…
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 tree ideals
Marcin Michalski, Robert Rałowski, Szymon Żeberski
In this paper we consider a notion of nonmeasurablity with respect to Marczewski and Marczewski-like tree ideals , , , and . We show that there exists a subset…
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…
Some properties of -Luzin sets
Marcin Michalski, Szymon Żeberski
In this paper we consider a notion of -Luzin set which generalizes the classical notion of Luzin set and Sierpi{ń}ski set on Euclidean spaces. We show that there is a…
Classifying invariant -ideals with analytic base on good Cantor measure spaces
Taras Banakh, Robert Ralowski, Szymon Zeberski
Let be a zero-dimensional compact metrizable space endowed with a strictly positive continuous Borel -additive measure which is good in the sense that for any clopen sub…
Luzin and Sierpiński sets, some nonmeasurable subsets of the plane and additive properties on the line
Marcin Michalski, Szymon Żeberski
In this paper we shall introduce some nonmeasurable and completely nonmeasurable subsets of the plane with various additional properties, e.g. being Hamel basis, intersecting each…
Group actions on Polish spaces
Robert Rałowski, Szymon Żeberski
In this paper we investigate the action of Polish groups (not necessary abelian) on an uncountable Polish spaces. We consider two main situations. First, when the orbits given by g…
Topologically invariant -ideals on the Hilbert cube
Taras Banakh, Michal Morayne, Robert Ralowski +1
We study and classify topologically invariant -ideals with a Borel base on the Hilbert cube and evaluate their cardinal characteristics. One of the results of this paper solves…
Topologically invariant σ-ideals on Euclidean spaces
Taras Banakh, Michał Morayne, Robert Rałowski +1
We study and classify topologically invariant sigma-ideals with an analytic base on Euclidean spaces and evaluate the cardinal characteristics of such ideals.
Complete nonmeasurability in regular families
Robert Ralowski, Szymon Zeberski
We show that for a -ideal $\ci$ with a Borel base of subsets of an uncountable Polish space, if $\ca$ is (in several senses) a "regular" family of subsets from $\ci $ then there…
Bernstein sets and -coverings
J. Kraszewski, R. Ralowski, P. Szczepaniak +1
In this paper we study a notion of a -covering in connection with Bernstein sets and other types of nonmeasurability. Our results correspond to those obtained by Muthuvel and No…
Completely nonmeasurable unions
Robert Ralowski, Szymon Zeberski
Assume that there is no quasi-measurable cardinal smaller than . ( is quasi measurable if there exists -additive ideal $\ci $ of subsets of such that the Boolean alg…
Generalized Luzin sets
Robert Ralowski, Szymon Zeberski
In this paper we invastigate the notion of generalized (I,J) - Luzin set. This notion generalize the standard notion of Luzin set and Sierpinski set. We find set theoretical condit…