5 papers
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…
Scales, products and the second row of the Scheepers diagram
Michał Pawlikowski, Piotr Szewczak, Lyubomyr Zdomskyy
We consider products of sets of reals with a combinatorial structure based on scales parameterized by filters. Sets of this kind have been extensively investigated in products of s…
On strong algebrability of families of non-measurable functions of two variables
Szymon Głcab, Mateusz Lichman, Michał Pawlikowski
Recently Tomasz Natkaniec in [On lineability of families of non-measurable functions of two variable. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 115(1):Paper No. 33…
Free group of Hamel functions
Mateusz Lichman, Michał Pawlikowski, Szymon Smolarek +1
We construct a free group of continuum many generators among those autobijections of which are also Hamel bases of , with identity function included. We…
An inverse Fraïssé limit for finite posets and duality for posets and lattices
Szymon Głcab, Michał Pawlikowski
We consider a category of all finite partial orderings with quotient maps as arrows and construct a Fraïssé sequence in this category. Then we use commonly known relations between…