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It is well-known that topological bases in Banach spaces are stable, in the sense that small perturbation of basis elements preserves the basis property of the system. We show that, for Frechet spaces, the situation may differ. For each compact set K of infinite cardinality with an isolated point, the space of Whitney jets on K does not possess a polynomial basis. On the other hand, polynomials are dense in any Whitney space. Thus, in general, topological bases in Frechet spaces are not stable.