Products of Luzin-type sets with combinatorial properties

Piotr Szewczak, Grzegorz Wiśniewski

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We construct Luzin-type subsets of the real line in all finite powers Rothberger, with a non-Menger product. To this end, we use a purely combinatorial approach which allows to weaken assumptions used earlier to construct sets with analogous properties. Our assumptions hold, e.g., in the Random model, where already known category theoretic methods fail.

Original languageEnglish
Pages (from-to)420-433
Number of pages14
JournalTopology and its Applications
StatePublished - 1 Sep 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 Elsevier B.V.


  • Luzin set
  • Menger property
  • Product space
  • Rothberger property
  • Scales
  • Scheepers property


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