5 papers
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…
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…