The $\pi$-property of a Banach space along a filter

Jaros{\l}aw Swaczyna; Tomasz Kania

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The π-property of a Banach space along a filter

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arxiv 2508.21242 v1 pith:4KFCFLJ4 submitted 2025-08-28 math.FA math.LO

The π-property of a Banach space along a filter

Tomasz Kania , Jaros{\l}aw Swaczyna This is my paper

classification math.FA math.LO

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We examine the analyticity of the class of separable Banach spaces possessing the $\pi$-property, defined in terms of convergence along a filter. Our results establish that this class is $\Sigma^1_3$ whenever the underlying filter is analytic (as a subset of the Cantor set $\Delta$). Furthermore, we demonstrate that if the filter is countably generated, the class of such spaces is $\Sigma^1_2$ with respect to any admissible Polish topology on the family of closed subspaces of $C(\Delta)$.

The π-property of a Banach space along a filter

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