On Borel sets in ideal topologies
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912788104871936 |
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| author | Moreno, Miguel Pitton, Beatrice |
| author_facet | Moreno, Miguel Pitton, Beatrice |
| contents | We study the Borel and analytic subsets of the spaces \({}^κκ\) and \({}^κ2\) endowed with ideal topologies, where \(κ\) is a regular uncountable cardinal. We establish that the Borel hierarchy does not collapse in any ideal topology and prove that every Borel set in such a topology is analytic. In particular, when the ideal contains an unbounded set, the class of analytic sets coincides with the entire powerset. Furthermore, we show that the Approximation Lemma holds for ideal topologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21140 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Borel sets in ideal topologies Moreno, Miguel Pitton, Beatrice Logic General Topology 03E15 (Primary) 03E05, 54A05, 54E99 (Secondary) We study the Borel and analytic subsets of the spaces \({}^κκ\) and \({}^κ2\) endowed with ideal topologies, where \(κ\) is a regular uncountable cardinal. We establish that the Borel hierarchy does not collapse in any ideal topology and prove that every Borel set in such a topology is analytic. In particular, when the ideal contains an unbounded set, the class of analytic sets coincides with the entire powerset. Furthermore, we show that the Approximation Lemma holds for ideal topologies. |
| title | On Borel sets in ideal topologies |
| topic | Logic General Topology 03E15 (Primary) 03E05, 54A05, 54E99 (Secondary) |
| url | https://arxiv.org/abs/2512.21140 |