4 citations · 10 across the 24 of their papers we have counts for
11 papers · 1 filter
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…
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…
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…