diffeology

diffeology (plural diffeologies)

1. (differential geometry) The set of smooth parametrizations of a given set ${\displaystyle X}$; the set of smooth maps ${\displaystyle S\rightarrow X}$, where ${\displaystyle S}$ is any open set ${\displaystyle \subseteq \mathbb {R} ^{n}}$; the theory of such constructs.
   • 2007, Jan Kubarski, Geometry and Topology of Manifolds: The Mathematical Legacy of Charles Ehresmann; on the Occasion of the Hundredth Anniversary of His Birthday, page 358:

     In this case, ${\displaystyle A}$ and ${\displaystyle f(A)}$ are both D-open and ${\displaystyle f:A\rightarrow f(A)}$ is a diffeomorphism where ${\displaystyle A}$ and ${\displaystyle f(A)}$ are equipped with their subset diffeology.

   • 2010, Patrick Iglesias-Zemmour, The Moment Maps in Diffeology, American Mathematical Society, page 32:

     And, for ${\displaystyle {\mathcal {G}}^{*}/\Gamma }$ and ${\displaystyle {\mathcal {G}}'^{*}/\Gamma '}$ equipped with the quotient diffeologies, ${\displaystyle h_{\Gamma }^{*}}$ is naturally smooth.

• 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 plot.
• A set together with a diffeology is called a diffeological space.

• quotient diffeology

• diffeological

• diffeological space

• diffeology on Wikipedia.Wikipedia