Critical ideals for compact spaces
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912277304705024 |
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| author | Filipów, Rafał Kowalczuk, Małgorzata Kwela, Adam |
| author_facet | Filipów, Rafał Kowalczuk, Małgorzata Kwela, Adam |
| contents | For each countable ordinal $α$, we introduce an ideal $conv_α$ and use it to characterize the class of all compact countable spaces which are homeomorphic to the space $ω^α\cdot n+1$ with the order topology. The characterization is expressed in terms of finding a convergent subsequence defined on a set not belonging to $conv_α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12571 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Critical ideals for compact spaces Filipów, Rafał Kowalczuk, Małgorzata Kwela, Adam General Topology 54A20, 03E05 (Primary) 03E10, 03E15, 03E17, 03E75, 40A05, 54H05 (Secondary) For each countable ordinal $α$, we introduce an ideal $conv_α$ and use it to characterize the class of all compact countable spaces which are homeomorphic to the space $ω^α\cdot n+1$ with the order topology. The characterization is expressed in terms of finding a convergent subsequence defined on a set not belonging to $conv_α$. |
| title | Critical ideals for compact spaces |
| topic | General Topology 54A20, 03E05 (Primary) 03E10, 03E15, 03E17, 03E75, 40A05, 54H05 (Secondary) |
| url | https://arxiv.org/abs/2503.12571 |