21 citations · 22 across the 13 of their papers we have counts for
20 papers
On disjoint tilings of by star-shaped bodies
Piotr Koszmider, Piotr Szewczak
We employ the set-theoretic methods yielding the consistency of the existence of nontrivial pairwise disjoint covers of the unit interval (or equivalently for $n\in\…
Combinatorial covering properties in an uncountable setting: canonical examples
Ayelet Amsalem, Adi Jarden, Michał Pawlikowski +3
We provide examples of spaces satisfying generalized combinatorial covering properties such as the Hurewicz, Menger, and -properties in an uncountable setting. Our approach is m…
Productively Scheepers spaces and their relatives
Marta Kładź-Duda, Piotr Szewczak, Lyubomyr Zdomskyy
We prove that assuming , in the class of hereditarily Lindelöf spaces, each productively Scheepers space is productively Hurewicz. The above statement re…
Universally meager sets in the Miller model and similar ones
Valentin Haberl, Piotr Szewczak, Lyubomyr Zdomskyy
We work in the realm of sets of reals. We prove that in the Miller model and in a model constructed by Goldstern-Judah-Shelah all universally meager sets have size at most . S…
Totally paracompact spaces and the Menger covering property
Davide Giacopello, Maddalena Bonanzinga, Piotr Szewczak
A topological space is totally paracompact if any base of this space contains a locally finite subcover. We focus on a problem of Curtis whether in the class of regular Lindelöf sp…
Concentrated sets and the Hurewicz property
Valentin Haberl, Piotr Szewczak, Lyubomyr Zdomskyy
A set of reals is -concentrated if it has cardinality at least and it contains a countable set such that each closed subset of d…
Scales, products and the second row of the Scheepers diagram
Michał Pawlikowski, Piotr Szewczak, Lyubomyr Zdomskyy
We consider products of sets of reals with a combinatorial structure based on scales parameterized by filters. Sets of this kind have been extensively investigated in products of s…
Small Hurewicz and Menger sets which have large continuous images
Piotr Szewczak, Tomasz Weiss, Lyubomyr Zdomskyy
We provide new techniques to construct sets of reals without perfect subsets and with the Hurewicz or Menger covering properties. In particular, we show that if the Continuum Hypot…
Menger and consonant sets in the Sacks model
Valentin Haberl, Piotr Szewczak, Lyubomyr Zdomskyy
Using iterated Sacks forcing and topological games, we prove that the existence of a totally imperfect Menger set in the Cantor cube with cardinality continuum is independent from…
Concentrated sets and -sets in the Miller model
Valentin Haberl, Piotr Szewczak, Lyubomyr Zdomskyy
Using combinatorial covering properties, we show that there is no concentrated set of reals of size in the Miller model. The main result refutes a conjecture of Bartoszyński…
Abstract colorings, games and ultrafilters
Piotr Szewczak
The main result provide a common generalization for Ramsey-type theorems concerning finite colorings of edge sets of complete graphs with vertices in infinite semigroups. We captur…
Null sets and combinatorial covering properties
Piotr Szewczak, Tomasz Weiss
A subset of the Cantor cube is null-additive if its algebraic sum with any null set is null. We construct a set of cardinality continuum such that: all continuous images of the set…
Unbounded towers and products
Piotr Szewczak, Magdalena Włudecka
We investigate products of sets of reals with combinatorial covering properties. A topological space satisfies if for each sequence of point-cofinite open cover…
Strongly sequentially separable function spaces, via selection principles
Alexander V. Osipov, Piotr Szewczak, Boaz Tsaban
A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. We consider this and re…
Products of Luzin-type sets with combinatorial properties
Piotr Szewczak, Grzegorz Wiśniewski
We construct Luzin-type subsets of the real line in all finite powers Rothberger, with a non-Menger product. To this end, we use a purely combinatorial approach which allows to wea…
Finite powers and products of Menger sets
Piotr Szewczak, Boaz Tsaban, Lyubomyr Zdomskyy
We construct, using mild combinatorial hypotheses, a real Menger set that is not Scheepers, and two real sets that are Menger in all finite powers, with a non-Menger product. By a…
The Haar Measure Problem
Adam J. Przeździecki, Piotr Szewczak, Boaz Tsaban
An old problem asks whether every compact group has a Haar-nonmeasurable subgroup. A series of earlier results reduce the problem to infinite metrizable profinite groups. We provid…
A classification of the cofinal structures of precompacta
Aviv Eshed, M. Vincenta Ferrer, Salvador Hernández +2
We provide a complete classification of the possible cofinal structures of the families of precompact (totally bounded) sets in general metric spaces, and compact sets in general c…
Products of general Menger spaces
Piotr Szewczak, Boaz Tsaban
We study products of general topological spaces with Menger's covering property, and its refinements based on filters and semifilters. To this end, we extend the projection method…
Products of Menger spaces: a combinatorial approach
Piotr Szewczak, Boaz Tsaban
We construct Menger subsets of the real line whose product is not Menger in the plane. In contrast to earlier constructions, our approach is purely combinatorial. The set theoretic…