32 citations · 260 across the 75 of their papers we have counts for
6 papers · 1 filter
Construction under Martin's axiom of a Boolean algebra with the Grothendieck property but without the Nikodym property
Damian Sobota, Lyubomyr Zdomskyy
Improving a result of M. Talagrand, under the assumption of a weak form of Martin's axiom, we construct a totally disconnected compact Hausdorff space such that the Banach spac…
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…