Diffeology

Diffeology is a branch of mathematics that generalizes the notion of smooth manifolds. It was introduced by Jean-Marie Dufour and his collaborators in the 1980s to provide a more flexible framework for studying smooth structures on spaces that may not have a well-defined manifold structure. In traditional differential geometry, a smooth manifold is defined as a topological space that locally resembles Euclidean space and has a compatible smooth structure.