Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Szewczak, Piotr"'
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 Hypothesis holds, then there are such sets which can be mapped continuously
Externí odkaz:
http://arxiv.org/abs/2406.12609
Using an iterated Sacks forcing and topological games, we prove that the existence of a totally imperfect Menger set in the Cantor cube with cardinality continuum, is independent from ZFC. We also analyze structures of Hurewicz or consonant subsets o
Externí odkaz:
http://arxiv.org/abs/2406.05457
Using combinatorial covering properties, we show that there is no concentrated set of reals of size $\omega_2$ in the Miller model. The main result refutes a conjecture of Bartoszy\'{n}ski and Halbeisen. We also prove that there are no $\gamma$-set o
Externí odkaz:
http://arxiv.org/abs/2310.03864
Autor:
Szewczak, Piotr
The main result provide a common generalization for Ramsey-type theorems concerning finite colorings of edge sets of complete graphs with vertices in infinite semigroups. We capture the essence of theorems proved in different fields: for natural numb
Externí odkaz:
http://arxiv.org/abs/2107.02830
Autor:
Szewczak, Piotr, Weiss, Tomasz
A subset of the Cantor cube is null-additive if its algebraic sum with any null set is null. We construct a set of cardinality continuum such that: all continuous images of the set into the Cantor cube are null-additive, it contains a homeomorphic co
Externí odkaz:
http://arxiv.org/abs/2006.10796
Autor:
Szewczak, Piotr, Włudecka, Magdalena
We investigate products of sets of reals with combinatorial covering properties. A topological space satisfies $\mathsf{S}_1(\Gamma,\Gamma)$ if for each sequence of point-cofinite open covers of the space, one can pick one element from each cover and
Externí odkaz:
http://arxiv.org/abs/1912.02528
A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. We consider this and related properties, for the spaces of continous and Borel real-valued fu
Externí odkaz:
http://arxiv.org/abs/1905.08070
Autor:
Szewczak, Piotr, Tsaban, Boaz
We provide conceptual proofs of the two most fundamental theorems concerning topological games and open covers: Hurewicz's Theorem concerning the Menger game, and Pawlikowski's Theorem concerning the Rothberger game.
Comment: Submitted for publi
Comment: Submitted for publi
Externí odkaz:
http://arxiv.org/abs/1904.02736
Autor:
Szewczak, Piotr, Wiśniewski, Grzegorz
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 properti
Externí odkaz:
http://arxiv.org/abs/1903.05208