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Erdős problem 1151

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Let Lnf\mathcal{L}^nf be the Lagrange interpolation polynomials of a continuous ff on the Chebyshev nodes. Prove that, for any closed A⊆[−1,1]A\subseteq [-1,1], there exists a continuous function ff such that AA is the set of limit points of Lnf(x)\mathcal{L}^nf(x).

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