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Publikováno v:
Fundamenta Mathematicae. 253:257-275
We construct, using mild combinatorial hypotheses, a real Menger set that is not Scheepers, and two real sets that are Menger in all finite powers, with a non-Menger product. By a forcing-theoretic argument, we show that the same holds in the Blass--
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2c0b0ed002ea27fde614a46fa913a4f1
https://doi.org/10.4064/fm896-4-2020
https://doi.org/10.4064/fm896-4-2020
Autor:
Boaz Tsaban, Piotr Szewczak
Publikováno v:
Topology and its Applications. 255:41-55
We study, in a systematic manner, products of general topological spaces with Menger's covering property, and its refinements based on filters and semifilters. To this end, we apply Dedekind compactification to extend the projection method from the c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7b3d648786a62e5791b9933109e000cd
https://doi.org/10.1016/j.topol.2019.01.005
https://doi.org/10.1016/j.topol.2019.01.005
Autor:
Piotr Szewczak
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0a4ca4ad99b11600c3d06f08f125e29d
Autor:
Piotr Szewczak, Tomasz Weiss
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::10711ed293376efeaddb7d12ff9b9960
Publikováno v:
Repositori Universitat Jaume I
Universitat Jaume I
Universitat Jaume I
We provide a complete classification of the possible cofinal structures of the families of precompact (totally bounded) sets in general metric spaces, and compact sets in general complete metric spaces. Using this classification, we classify the cofi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b28379b0a3126c7e9d8df4bbe5ea07f5
http://hdl.handle.net/10234/189225
http://hdl.handle.net/10234/189225
Autor:
Piotr Szewczak
Publikováno v:
Topology and its Applications. 222:254-273
One of the most important problems concerning paracompactness is the characterization of productively paracompact spaces, i.e., the spaces whose product with every paracompact space is paracompact. To this end, an infinite topological game introduced
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3ce02530a6080d241a12ae35458c2a01
https://doi.org/10.1016/j.topol.2017.03.001
https://doi.org/10.1016/j.topol.2017.03.001
Autor:
Grzegorz Wiśniewski, Piotr Szewczak
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7668ddf99cda3d0c421bd6d6ff582a24
Autor:
Piotr Szewczak, Magdalena Włudecka
Publikováno v:
Annals of Pure and Applied Logic. 172:102900
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c0071fe0e851f372184bda3c8d730134
https://doi.org/10.1016/j.apal.2020.102900
https://doi.org/10.1016/j.apal.2020.102900
Autor:
Piotr Szewczak, Boaz Tsaban
Publikováno v:
Topology and its Applications. 272:107048
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.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c2b4bd64fcc1dfdabde012033e672b27
https://doi.org/10.1016/j.topol.2019.107048
https://doi.org/10.1016/j.topol.2019.107048