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arXiv · 2502.17001

Polyhedrality for twisted sums with $C(ω^α)$

Jesús M. F. Castillo·Alberto Salguero Alarcón
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Abstract

We obtain two partial answers to the 3-space problem for isomorphic polyhedrality: (1) every twisted sum of $C(α)$, $α<ω_1$, with a separable isomorphically polyhedral space with the BAP, is isomorphically polyhedral. (2) Every twisted sum of $c_0(κ)$ and a Banach space having a boundary with property $(*)$ has a boundary with property $(*)$, hence it is isomorphically polyhedral.

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Jesús M. F. Castillo, Alberto Salguero Alarcón. 2025-03-11. Polyhedrality for twisted sums with $C(ω^α)$. https://arxiv.org/abs/2502.17001

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