14 papers
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 pa…
Combinatorial covering properties in an uncountable setting: canonical examples
Ayelet Amsalem, Adi Jarden, MichaÅ 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…
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 small Banach space without nice renormings
Todor Manev, Damian Sobota, Lyubomyr Zdomskyy
We prove that consistently and there exists a compact space whose Banach space of continuous real-valued functions is Grothendieck, has density $Ï_1…
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…
Productively Scheepers spaces and their relatives
Marta KÅadź-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 r…