Diffeomorphism

In mathematics, a diffeomorphism is an isomorphism in the category of smooth manifolds. It is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth. Given two manifolds M and N, a bijective map f from M to N is called a diffeomorphism if both and its inverse are differentiable (if these functions are r times continuously differentiable, f is called a C-diffeomorphism). Two ... more

In mathematics, a diffeomorphism is an isomorphism in the category of smooth manifolds. It is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth. Given two manifolds M and N, a bijective map f from M to N is called a diffeomorphism if both and its inverse are differentiable (if these functions are r times continuously differentiable, f is called a C-diffeomorphism). Two manifolds M and N are diffeomorphic (symbol usually being ) if there is a smooth bijective function f from M to N with smooth inverse. They are C diffeomorphic if there is an r times continuously differentiable bijective function between them whose inverse is also r times continuously differentiable. Given a subset X of a manifold M and a subset Y of a manifold N, a function is said to be smooth if for all there is a neighborhood of p and a smooth function such that the restrictions agree (note that g is an extension of f). We say that f... less