2025/03/24 by Michał Pawlikowski, Pawlikowski, Michał, Piotr Szewczak +3 · 1 citation
Computer Science · #05D10 #54C35 #54D20 #Combinatorics (math.CO) #FOS: Mathematics #General Topology (math.GN) #Model-Driven Software Engineering Techniques
paper · pdf · doi:10.48550/arxiv.2503.18615
openalex publication_date 2025/03/24 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
We consider products of sets of reals with a combinatorial structure based on scales parameterized by filters. This kind of sets were intensively investigated in products of spaces with combinatorial covering properties as Hurewicz, Scheepers, Menger and Rothberger. We will complete this picture with focusing on properties from the second row of the Scheepers diagram. In particular we show that in the Miller model a product space of two \mathfrakd-concentrated sets has a strong covering property S1(Γ,Ω). We provide also counterexamples in products to demonstrate limitations of used methods.