Polyhedrality for twisted sums with $C(\omega^\alpha )$
Studia Mathematica
MSC: Primary 46B03; Secondary 46M18, 54D30, 46B20
DOI: 10.4064/sm241009-20-3
Published online: 28 August 2025
Abstract
We obtain two partial answers to the $3$-space problem for isomorphic polyhedrality: (1) every twisted sum of $C(\alpha )$, $\alpha \lt \omega _1$, with a separable isomorphically polyhedral space with the BAP, is isomorphically polyhedral. (2) Every twisted sum of $c_0(\aleph )$ and a Banach space having a boundary with property $(*)$ has a boundary with property $(*)$, hence it is isomorphically polyhedral.
