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Barely alternating real almost chains and extension operators for compact lines

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arXiv:2403.19327v1 Announce Type: new
Abstract: Assume $\text{MA}(\kappa)$. We show that for every real chain of size $\kappa$ in the quotient Boolean algebra $P(\omega)/fin$ we can find an almost chain of representatives such that every $n\in\omega$ oscillates at most three times along the almost chain. This is used to show that for every countable discrete extension of a separable compact line $K$ of weight $\kappa$ there exists an extension operator $E:C(K)\longrightarrow C(L)$ of norm at most three.

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