Every (*) analytic function has this property, but examples of functions with this property that are not analytic include the Fabius function and bump functions.
In algebraic geometry, a morphism between schemes is etale if it is both unramified and this. Heisuke Hironaka showed that, over a field of characteristic 0, every algebraic variety is birational to a projective variety with this property. Algebraic varieties are said to be this if they have no singular points. An integer is said to be this if it has no large prime factors. In analysis, mollifiers are used to create sequences of functions with this property. Frolicher spaces attempt to generalize the class of manifolds with this property. A complex-valued function with this property can generate another set of complex-valued functions with this property in a particular way according to Borel's lemma. Every (*) analytic function has this property, but examples of functions with this property that are not analytic include the Fabius function and bump functions. For 10 points, what is this word describing a function which has derivatives of every order?
In algebraic geometry, a morphism between schemes is etale if it is both unramified and this.
smoothness [prompt on “infinitely differentiable” or “differentiable”; accept flat before “birational”]