5 citations · 18 across the 22 of their papers we have counts for
24 papers
Journey into special -spaces
Robert Rałowski
In this survey, we review certain types of special \(T_{1}\) spaces and their associated fixed-point theorems. Kupka introduced the notion of a feeble topological contraction, whic…
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}\}…
Fixed point theorems for topological contractions and the Hutchinson operator
Michał Morayne, Robert Rałowski
For a topological space a topological contraction on is a closed mapping such that for every open cover of there is a positive integer such that the imag…
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…
A note on Hutchinson operator in compact topological spaces
Michał Morayne, Robert Rałowski
In compact topological spaces the Hutchinson operator of a contractive IFS (iterated function system; a finite family of closed mappings from the space into itself) may not b…
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…
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…
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…
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 -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…
Remarks on nonmeasurable unions of big point families
Robert Ralowski
We show that under some conditions on a family $\mathcal{A}\subset\bbi$ there exists a subfamily such that is nonmeasurabl…
Nonmeasurability in Banach spaces
Robert Ralowski
We show that for a -ideal $\ci$ with a Steinhaus property defined on Banach space, if two non-homeomorphic Banach with the same cardinality of the Hamel basis then there is a $\…
Wick algebras approach to physics of 2D systems
Roman Gielerak, Robert Ralowski
The notion of anyonic Wick algebras is introduced and the corresponding second quantisation procedure is discussed. Applications to the physics of 2D anyonic matter are presented.…
On Deformations of Commutation Relation Algebras
Robert Rałowski
This paper is on - symmetric creation and annihilation operators, which are constructed on Wick's algebras which fulfil consistency conditions. The essential assumption is that…