Denjoy-Carleman classes and lineability

The Denjoy-Carleman classes are spaces of smooth functions which satisfy growth conditions on their derivatives defined through weight sequences. In this talk, given a Denjoy-Carleman class E of Beurling type that strictly contains another non-quasianalytic class F of Roumieu type, we handle the question of knowing how large the set of functions in E that are nowhere in the class F is. In particular, we prove the dense-lineability of the set of functions of E which are nowhere in F. Consequences for the Gevrey classes are also given. We extend then these results to the case of classes of ultradifferentiable functions defined using weight functions.