Scales, products and the second row of the Scheepers diagram
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913762025406464 |
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| author | Pawlikowski, Michał Szewczak, Piotr Zdomskyy, Lyubomyr |
| author_facet | Pawlikowski, Michał Szewczak, Piotr Zdomskyy, Lyubomyr |
| contents | 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 $\mathfrak{d}$-concentrated sets has a strong covering property $\mathsf{S}_1(Γ,Ω)$. We provide also counterexamples in products to demonstrate limitations of used methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18615 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scales, products and the second row of the Scheepers diagram Pawlikowski, Michał Szewczak, Piotr Zdomskyy, Lyubomyr Combinatorics General Topology 54D20, 05D10, 54C35 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 $\mathfrak{d}$-concentrated sets has a strong covering property $\mathsf{S}_1(Γ,Ω)$. We provide also counterexamples in products to demonstrate limitations of used methods. |
| title | Scales, products and the second row of the Scheepers diagram |
| topic | Combinatorics General Topology 54D20, 05D10, 54C35 |
| url | https://arxiv.org/abs/2503.18615 |