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