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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.12041 |
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| _version_ | 1866912830015406080 |
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| author | Filipów, Rafał Kowalczuk, Małgorzata Książek, Hubert Kwela, Adam Ucal, Grzegorz |
| author_facet | Filipów, Rafał Kowalczuk, Małgorzata Książek, Hubert Kwela, Adam Ucal, Grzegorz |
| contents | We study ideal-based refinements of sequential compactness arising from the class FinBW(I), consisting of topological spaces in which every sequence admits a convergent subsequence indexed by a set outside a given ideal I. A central theme of this work is the existence of critical ideals whose position in the Katetov order determines the relationship between a fixed class of spaces and the corresponding FinBW(I) classes. Building on earlier results characterizing several classical topological classes via such ideals, we extend this theory to a broader framework based on partition regular functions, which unifies ordinary convergence with other non-classical convergence notions such as IP- and Ramsey-type convergence. Furthermore, we investigate the existence of critical ideals associated with function classes motivated by Mazurkiewicz's theorem on uniformly convergent subsequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12041 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Critical partition regular functions for compact spaces Filipów, Rafał Kowalczuk, Małgorzata Książek, Hubert Kwela, Adam Ucal, Grzegorz General Topology 54A20, 03E75 (Primary) 40A35 (Secondary) We study ideal-based refinements of sequential compactness arising from the class FinBW(I), consisting of topological spaces in which every sequence admits a convergent subsequence indexed by a set outside a given ideal I. A central theme of this work is the existence of critical ideals whose position in the Katetov order determines the relationship between a fixed class of spaces and the corresponding FinBW(I) classes. Building on earlier results characterizing several classical topological classes via such ideals, we extend this theory to a broader framework based on partition regular functions, which unifies ordinary convergence with other non-classical convergence notions such as IP- and Ramsey-type convergence. Furthermore, we investigate the existence of critical ideals associated with function classes motivated by Mazurkiewicz's theorem on uniformly convergent subsequences. |
| title | Critical partition regular functions for compact spaces |
| topic | General Topology 54A20, 03E75 (Primary) 40A35 (Secondary) |
| url | https://arxiv.org/abs/2601.12041 |