Concept

Diffeology

Résumé
In mathematics, a diffeology on a set generalizes the concept of smooth charts in a differentiable manifold, declaring what the "smooth parametrizations" in the set are. The concept was first introduced by Jean-Marie Souriau in the 1980s under the name Espace différentiel and later developed by his students Paul Donato and Patrick Iglesias. A related idea was introduced by Kuo-Tsaï Chen (陳國才, Chen Guocai) in the 1970s, using convex sets instead of open sets for the domains of the plots. Intuitive definition Recall that a topological manifold is a topological space which is locally homeomorphic to \mathbb{R}^n. Differentiable manifolds generalize the notion of smoothness on \mathbb{R}^n in the following sense: a differentiable manifold is a topological manifold with a differentiable atlas, i.e. a collection of maps from open subsets of \mathbb{R}^n to the manifold which are used to "pull back" the differential structure from \m
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