Given two differentiable manifolds and bijective map mathf/math from to is called a diffeomorphism if both mathf:M\to N/math and its inverse mathf^{-1}:N\to M/math are smooth functions.

Given two differentiable manifolds and bijective map mathfmath from to is called a diffeomorphism if both mathf:M\to Nmath and its inverse mathf^{-1}:N\to Mmath are smooth.

Given two differentiable manifolds ''M'' and ''N'', a bijective map f from ''M'' to ''N'' is called a diffeomorphism if both f:M\to N and its inverse f^{-1}:N\to M are smooth function

In mathematics, a diffeomorphism is a kind of isomorphism 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.