Diffeology

In mathematics, a diffeology on a set generalizes the concept of a smooth atlas of a differentiable manifold, by declaring only what constitutes the "smooth parametrizations" into the set. A diffeological space is a set equipped with a diffeology. Many of the standard tools of differential geometry extend to diffeological spaces, which beyond manifolds include arbitrary quotients of manifolds, arbitrary subsets of manifolds, and spaces of mappings between manifolds.