A compact set without Markov's property but with an extension operator for C∞-functions

Abstract

We give an example of a compact set K ⊂ [0,1] such that the space ε(K) of Whitney functions is isomorphic to the space s of rapidly decreasing sequences, and hence there exists a linear continuous extension operator L : ε(K) → C∞[0,1]. At the same time, Markov's inequality is not satisfied for certain polynomials on K.