Nonseparable $C(K)$ -spaces can be twisted when $K$ is a finite height compact

preprint2016arXivOpen access

We show that, given a nonmetrizable compact space $K$ having $ω$ -derived set empty, there always exist nontrivial exact sequences $0\to c_0\to E\to C(K)\to 0$ . This partially solves a problem posed in several papers: Is $Ext(C(K), c_0)\neq 0$ for $K$ a nonmetrizable compact set?

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Nonseparable $C(K)$ -spaces can be twisted when $K$ is a finite height compact

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Nonseparable C(K)C(K)C(K)-spaces can be twisted when KKK is a finite height compact

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Nonseparable $C(K)$ -spaces can be twisted when $K$ is a finite height compact