diffeology

Noun

 * 1)  The set of smooth parametrizations of a given set $$X$$; the set of smooth maps $$S\rightarrow X$$, where $$S$$ is any open set $$\subseteq\mathbb{R}^n$$; the theory of such constructs.

Usage notes

 * The dimensional qualifier n is not required to be the same for all members of the diffeology.
 * A member of a diffeology may be called a.
 * A set together with a diffeology is called a.