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We study the Gromov–Hausdorff and Kadets distances between $C(K)$-spaces and their quotients. We prove that if the Gromov–Hausdorff distance between $C(K)$ and $C(L)$ is less than $1/16$ then K and L are homeomorphic. If the Kadets distanc
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Dutrieux et al. (2005) studied this question.
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