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

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