32 citations · 260 across the 75 of their papers we have counts for
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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…
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 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…
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…
On some recent selective properties involving networks
Maddalena Bonanzinga, Davide Giacopello, Santi Spadaro +1
In this paper we investigate R-,H-, and M-{\it nw}-selective properties introduced in \cite{BG}. In particular, we provide consistent uncountable examples of such spaces and we def…
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…
Countable spaces, realcompactness, and the pseudointersection number
Claudio Agostini, Andrea Medini, Lyubomyr Zdomskyy
All spaces are assumed to be Tychonoff. Given a realcompact space , we denote by the smallest infinite cardinal such that is homeomorphic to a closed s…
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…
Selective separability properties of Fréchet-Urysohn spaces and their products
Serhii Bardyla, Fortunato Maesano, Lyubomyr Zdomskyy
In this paper we study the behaviour of selective separability properties in the class of Frechét-Urysohn spaces. We present two examples, the first one given in ZFC proves the exi…
On sequences of finitely supported measures related to the Josefson--Nissenzweig theorem
Witold Marciszewski, Damian Sobota, Lyubomyr Zdomskyy
Given a Tychonoff space , we call a sequence of signed Borel measures on a finitely supported Josefson--Nissenzweig sequence (in short a JN-s…
Open filters and measurable cardinals
Serhii Bardyla, Jaroslav Supina, Lyubomyr Zdomskyy
In this paper, we investigate the poset of free open filters on a given space . In particular, we characterize spaces for which is a lattice. F…
Ideal approach to convergence in functional spaces
Serhii Bardyla, Jaroslav Supina, Lyubomyr Zdomskyy
We solve the last standing open problem from the seminal paper by J. Gerlits and Zs. Nagy, which was later reposed by A. Miller, T. Orenshtein and B. Tsaban. Namely, we show that u…
On complemented copies of the space in spaces
Jerzy Kąkol, Witold Marciszewski, Damian Sobota +1
Cembranos and Freniche proved that for every two infinite compact Hausdorff spaces and the Banach space of continuous real-valued functions on en…
On regular separable countably compact -rigid spaces
Serhii Bardyla, Lyubomyr Zdomskyy
A topological space is said to be {\em -rigid} if any continuous map is constant. In this paper we construct a number of examples of regular countably com…
A countably compact topological group with the non-countably pracompact square
Serhii Bardyla, Alex Ravsky, Lyubomyr Zdomskyy
Under Martin's Axiom we construct a Boolean countably compact topological group whose square is not countably pracompact.
Preservation of -spaces and covering properties of products
Dušan Repovš, Lyubomyr Zdomskyy
We prove that the Hurewicz property is not preserved by finite products in the Miller model. This is a consequence of the fact that Miller forcing preserves ground model -spaces…
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…
Products of Menger spaces in the Miller model
Lyubomyr Zdomskyy
We prove that in the Miller model the Menger property is preserved by finite products of metrizable spaces. This answers several open questions and gives another instance of the in…
Products of -separable spaces in the Laver model
Dušan Repovš, Lyubomyr Zdomskyy
We prove that in the Laver model for the consistency of the Borel's conjecture, the product of any two -separable spaces is -separable.
Completely Baire spaces, Menger spaces, and projective sets
Franklin D. Tall, Lyubomyr Zdomskyy
W. Hurewicz proved that analytic Menger sets of reals are -compact and that co-analytic completely Baire sets of reals are completely metrizable. It is natural to try to general…
Products of Hurewicz spaces in the Laver model
Dušan Repovš, Lyubomyr Zdomskyy
This article is devoted to the interplay between forcing with fusion and combinatorial covering properties. We illustrate this interplay by proving that in the Laver model for the…
Locally compact, -compact spaces
Peter Nyikos, Lyubomyr Zdomskyy
An -compact space is a space in which every closed discrete subspace is countable. We give various general conditions under which a locally compact, -compact space is …