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.

Introduction

Calculus on "smooth spaces"

The differential calculus on <math>\mathbb{R}^n</math>, or, more generally, on finite dimensional vector spaces, is one of the most impactful successes of modern mathematics. Fundamental to its basic definitions and theorems is the linear structure of the underlying space.

  • Patrick Iglesias-Zemmour: Diffeology (many documents)
  • diffeology.net Global hub on diffeology and related topics