is an analog of the tangent bundle for Fréchet manifolds. Tame Fréchet spaces Frequently the Fréchet spaces that arise in practical applications of the derivative enjoy an additional property: they are tame. Roughly speaking, a tame Fréchet space is one which is almost a Banach space. On tame spaces, it is possible to define a preferred class of mappings, known as tame maps. On the category of tame spaces under tame maps, the underlying topology is strong enough to support a fully fledged theory of differential topology. Within this context, many more techniques from calculus hold. In particular, there are versions of the inverse and implicit function theorems. See also References Banach spaces Differential calculus Euclidean geometry Functions and mappings Generalizations of the derivative Topological vector spaces