Noun
diffeomorphism (plural diffeomorphisms)
(mathematics) A differentiable homeomorphism (with differentiable inverse) between differentiable manifolds.
Connectedness For manifolds, the diffeomorphism group is usually not connected. Source: Internet
Definition Given two manifolds M and N, a differentiable map f : M → N is called a diffeomorphism if it is a bijection and its inverse f −1 : N → M is differentiable as well. Source: Internet
Consequently, a surface deformation or diffeomorphism of surfaces has the conformal property of preserving (the appropriate type of) angles. Source: Internet
; Fourth remark If Df x is a bijection at x then f is said to be a local diffeomorphism (since, by continuity, Df y will also be bijective for all y sufficiently close to x). Source: Internet
Every diffeomorphism is a homeomorphism, but not every homeomorphism is a diffeomorphism. Source: Internet
Extensions of diffeomorphisms In 1926, Tibor Radó asked whether the harmonic extension of any homeomorphism or diffeomorphism of the unit circle to the unit disc yields a diffeomorphism on the open disc. Source: Internet