On Sierpiński sets, Hurewicz spaces and Hilgers functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917959124910080 |
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| author | Marciszewski, Witold Pol, Roman Zakrzewski, Piotr |
| author_facet | Marciszewski, Witold Pol, Roman Zakrzewski, Piotr |
| contents | The Hurewicz property is a classical generalization of $σ$-compactness and Sierpiński sets (whose existence follows from CH) are standard examples of non-$σ$-compact Hurewicz spaces. We show, solving a problem stated by Szewczak and Tsaban, that for each Sierpiński set S of cardinality at least $\mathfrak b$ there is a Hurewicz space H with $S\times H$ not Hurewicz. Some other questions in the literature concerning this topic are also answered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13146 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Sierpiński sets, Hurewicz spaces and Hilgers functions Marciszewski, Witold Pol, Roman Zakrzewski, Piotr General Topology Logic 54D20, 54B10, 03E17 The Hurewicz property is a classical generalization of $σ$-compactness and Sierpiński sets (whose existence follows from CH) are standard examples of non-$σ$-compact Hurewicz spaces. We show, solving a problem stated by Szewczak and Tsaban, that for each Sierpiński set S of cardinality at least $\mathfrak b$ there is a Hurewicz space H with $S\times H$ not Hurewicz. Some other questions in the literature concerning this topic are also answered. |
| title | On Sierpiński sets, Hurewicz spaces and Hilgers functions |
| topic | General Topology Logic 54D20, 54B10, 03E17 |
| url | https://arxiv.org/abs/2503.13146 |