9 papers
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…
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…
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 .…
Totally paracompact spaces and the Menger covering property
Davide Giacopello, Maddalena Bonanzinga, Piotr Szewczak
A topological space is totally paracompact if any base of this space contains a locally finite subcover. We focus on a problem of Curtis whether in the class of regular Lindelöf s…