Abstract
It is proven that any set E consisting of finitely many intervals can be approximated with order 1 / n by polynomial inverse images of [ - 1 , 1 ] . This leads to a new proof of the fact that the n-th Chebyshev constant is ⩽ K cap ( E ) n with some K independent of n. The proof uses properties of monotone systems, in particular, the statement in the so-called inheritance problem.
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