Given $a_1,\dots ,a_n\in [-1,1]$ let$${\mathcal{L}}^{n}f(x)=\sum _{1\le i\le n}f(a_i){\ell }_i(x)$$be the unique polynomial of degree $n-1$ which agrees with $f$ on $a_i$ for $1\le i\le n$ (that is, the Lagrange interpolation polynomial).Let $a_i$ be the set of Chebyshev nodes. Prove that, for any closed $A\subseteq [-1,1]$, there exists a continuous function $f$ such that $A$ is the set of limit points of ${\mathcal{L}}^{n}f(x)$.