diffeology

plural diffeologies

1. differential geometryThe set of smooth parametrizations of a given set X; the set of smooth maps S→X, where S is any open set ⊆ℝⁿ; the theory of such constructs.

   In this case, A and f(A) are both D-open and f#58;A#92;rightarrowf(A) is a diffeomorphism where A and f(A) are equipped with their subset diffeology.

   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

   1 more example

   And, for #92;mathcal#123;G#125;#42;#47;#92;Gamma and #92;mathcal#123;G#125;'#42;#47;#92;Gamma' equipped with the quotient diffeologies, h#42;#95;#92;Gamma is naturally smooth.

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