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Local extension property for finite height spaces

Volume 245 / 2019

Claudia Correa, Daniel V. Tausk Fundamenta Mathematicae 245 (2019), 149-165 MSC: Primary 06E05, 54G12; Secondary 46E15. DOI: 10.4064/fm513-6-2018 Published online: 1 February 2019

Abstract

We introduce a new technique for the study of the local extension property (${\mathop {\rm LEP}}$) for boolean algebras and we use it to show that the clopen algebra of every compact Hausdorff space $K$ of finite height has $\mathop {\rm LEP}$. This implies, under appropriate additional assumptions on $K$ and Martin’s Axiom, that every twisted sum of $c_0$ and $C(K)$ is trivial, generalizing a recent result by Marciszewski and Plebanek.

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