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A C(K) Banach space which does not have the Schroeder–Bernstein property
We construct a totally disconnected compact Hausdorff space $K_+$ which has clopen subsets $K_+^{\prime\prime}\subseteq K_+^{\prime}\subseteq K_+$ such that $K_+^{\prime\prime}$ is homeomorphic to $K_+$ and hence $C(K_+^{\prime\prime})$ is isometric as