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arXiv · 1907.09743

Splitting chains, tunnels and twisted sums

Félix Cabello Sánchez·Antonio Avilés·Piotr Borodulin-Nadzieja·David Chodounský·Osvaldo Guzmán
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Abstract

We study splitting chains in $\mathscr{P}(ω)$, that is, families of subsets of $ω$ which are linearly ordered by $\subseteq^*$ and which are splitting. We prove that their existence is independent of axioms of $\mathsf{ZFC}$. We show that they can be used to construct certain peculiar Banach spaces: twisted sums of $C(ω^*)=\ell_\infty/c_0$ and $c_0(\mathfrak c)$. Also, we consider splitting chains in a topological setting, where they give rise to the so called tunnels.

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BibTeXRIS

Félix Cabello Sánchez, Antonio Avilés, Piotr Borodulin-Nadzieja, David Chodounský, Osvaldo Guzmán. 2019-07-23. Splitting chains, tunnels and twisted sums. https://arxiv.org/abs/1907.09743

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