Are scales Fréchet?
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911521645264896 |
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| author | Figueroa-Sierra, Raul Guzmán, Osvaldo Hrušák, Michael Kwela, Adam |
| author_facet | Figueroa-Sierra, Raul Guzmán, Osvaldo Hrušák, Michael Kwela, Adam |
| contents | We continue the study of Dow spaces of a $\mathfrak{b}$-scale, originally introduced by Alan Dow in "$π$-Weight and the Fréchet-Urysohn property" (Topology and its Applications, Vol. 174, pp. 56-61). We prove that it is consistent that all such spaces are Fréchet, but it is also consistent that none of them is. We use these spaces to exhibit (consistently) a $\triangle_{2}^{1}$ ideal that does not satisfy the Category Dichotomy. Finally, we prove that the Category Dichotomy holds for all co-analytic ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15567 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Are scales Fréchet? Figueroa-Sierra, Raul Guzmán, Osvaldo Hrušák, Michael Kwela, Adam General Topology 54A20, 54A35, 03E05, 03E17 We continue the study of Dow spaces of a $\mathfrak{b}$-scale, originally introduced by Alan Dow in "$π$-Weight and the Fréchet-Urysohn property" (Topology and its Applications, Vol. 174, pp. 56-61). We prove that it is consistent that all such spaces are Fréchet, but it is also consistent that none of them is. We use these spaces to exhibit (consistently) a $\triangle_{2}^{1}$ ideal that does not satisfy the Category Dichotomy. Finally, we prove that the Category Dichotomy holds for all co-analytic ideals. |
| title | Are scales Fréchet? |
| topic | General Topology 54A20, 54A35, 03E05, 03E17 |
| url | https://arxiv.org/abs/2603.15567 |