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Let $X\in E$, where $E$ is a Banach function space on $(0,1)$. Consider the interval $[-X,X]$ and generate it to a closed lattice ideal $I$ of $E$. We may renorm this ideal $I$ such that $[-X,X]$ is the unit ball. Why is $I$ lattice-isomorphic to $C(K)$? Here, $K$ is a compact space.

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