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

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