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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2508.21242 |
| Etiquetas: |
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- 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 $C(Δ)$.