32 citations · 260 across the 75 of their papers we have counts for
8 papers · 1 filter
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…
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…
A density counterpart of the Scheepers covering property
Leandro Aurichi, Fortunato Maesano, Lyubomyr Zdomskyy
We introduce a density counterpart of the Scheepers covering property and study its relations to known combinatorial density property. In par…
On cycle covers of infinite bipartite graphs
Leandro Aurichi, Paulo Magalhães Júnior, Lyubomyr Zdomskyy
Given a graph and a subset of vertices of with size at least two, we denote by the set of vertices of that have at least two neighbors in . We say tha…
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…
On the interplay between productively Menger and productively Hurewicz spaces in models of
Dušan D. Repovš, Lyubomyr Zdomskyy
This article is devoted to the interplay between productively Menger and productively Hurewicz subspaces of the Cantor space. In particular, we show that in the Laver model for the…
A note on uniform continuity of monotone functions
Roman Pol, Piotr Zakrzewski, Lyubomyr Zdomskyy
We prove that it is consistent with ZFC that for every non-decreasing function , each subset of of cardinality contains a set of cardinality…
Countable dense homogeneity and topological groups
Claudio Agostini, Andrea Medini, Lyubomyr Zdomskyy
Building on results of Medvedev, we construct a example of a non-Polish topological group that is countable dense homogeneous. Our example is a dense subgroup of $\m…