5 citations · 18 across the 22 of their papers we have counts for
8 papers · 1 filter
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}\}…
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…
Note on nonmeasurable unions
Robert Ralowski
In this note we consider an arbitrary families of sets of ideal introduced by Marczewski-Szpilrajn. We show that in any uncountable Polish space and under some combinator…
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…