Productively Scheepers spaces and their relatives
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908839346962432 |
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| author | Kładź-Duda, Marta Szewczak, Piotr Zdomskyy, Lyubomyr |
| author_facet | Kładź-Duda, Marta Szewczak, Piotr Zdomskyy, Lyubomyr |
| contents | We prove that assuming $\mathfrak{b}=\mathfrak{d}$, in the class of hereditarily Lindelöf spaces, each productively Scheepers space is productively Hurewicz. The above statement remains true in the class of all general topological spaces assuming that $\mathfrak{d}=\aleph_1$. To this end we use combinatorial methods and the Menger covering property parametrized by ultrafilters. We also show that if near coherence of filters holds, then the Scheepers property is equivalent to a Menger property parametrized by any ultrafilter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16046 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Productively Scheepers spaces and their relatives Kładź-Duda, Marta Szewczak, Piotr Zdomskyy, Lyubomyr General Topology 54D20, 03E17 We prove that assuming $\mathfrak{b}=\mathfrak{d}$, in the class of hereditarily Lindelöf spaces, each productively Scheepers space is productively Hurewicz. The above statement remains true in the class of all general topological spaces assuming that $\mathfrak{d}=\aleph_1$. To this end we use combinatorial methods and the Menger covering property parametrized by ultrafilters. We also show that if near coherence of filters holds, then the Scheepers property is equivalent to a Menger property parametrized by any ultrafilter. |
| title | Productively Scheepers spaces and their relatives |
| topic | General Topology 54D20, 03E17 |
| url | https://arxiv.org/abs/2602.16046 |