The $π$-property of a Banach space along a filter
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908509384212480 |
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| author | Kania, Tomasz Swaczyna, Jarosław |
| author_facet | Kania, Tomasz Swaczyna, Jarosław |
| contents | We examine the analyticity of the class of separable Banach spaces possessing the $π$-property, defined in terms of convergence along a filter. Our results establish that this class is $Σ^1_3$ whenever the underlying filter is analytic (as a subset of the Cantor set $Δ$). Furthermore, we demonstrate that if the filter is countably generated, the class of such spaces is $Σ^1_2$ with respect to any admissible Polish topology on the family of closed subspaces of $C(Δ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $π$-property of a Banach space along a filter Kania, Tomasz Swaczyna, Jarosław Functional Analysis Logic 46B15 (Primary), 03E15 (Secondary) We examine the analyticity of the class of separable Banach spaces possessing the $π$-property, defined in terms of convergence along a filter. Our results establish that this class is $Σ^1_3$ whenever the underlying filter is analytic (as a subset of the Cantor set $Δ$). Furthermore, we demonstrate that if the filter is countably generated, the class of such spaces is $Σ^1_2$ with respect to any admissible Polish topology on the family of closed subspaces of $C(Δ)$. |
| title | The $π$-property of a Banach space along a filter |
| topic | Functional Analysis Logic 46B15 (Primary), 03E15 (Secondary) |
| url | https://arxiv.org/abs/2508.21242 |