Topology and category for singular product spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910207219597312 |
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| author | Hayashi, Yusuke van der Vlugt, Tristan |
| author_facet | Hayashi, Yusuke van der Vlugt, Tristan |
| contents | For $κ$ a regular uncountable cardinal, the higher Baire and Cantor spaces ${}^κκ$ and ${}^\kappa2$ (endowed with the ${<}κ$-box topology) have been relatively well-studied, but less is known about the case where $κ$ is singular. We will consider several spaces of functions and box topologies that could serve as higher Baire and Cantor spaces for singular cardinals. The ultimate focus of the article lies in studying cardinal characteristics of the ideal of $κ$-meagre subsets of these spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09582 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topology and category for singular product spaces Hayashi, Yusuke van der Vlugt, Tristan Logic General Topology 03E17 03E35 03E05 54B10 54A25 54C35 For $κ$ a regular uncountable cardinal, the higher Baire and Cantor spaces ${}^κκ$ and ${}^\kappa2$ (endowed with the ${<}κ$-box topology) have been relatively well-studied, but less is known about the case where $κ$ is singular. We will consider several spaces of functions and box topologies that could serve as higher Baire and Cantor spaces for singular cardinals. The ultimate focus of the article lies in studying cardinal characteristics of the ideal of $κ$-meagre subsets of these spaces. |
| title | Topology and category for singular product spaces |
| topic | Logic General Topology 03E17 03E35 03E05 54B10 54A25 54C35 |
| url | https://arxiv.org/abs/2605.09582 |