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A '''diffeomorphism''' is an infinitely [[derivative|differentiable]] [[homeomorphism]] with an infinitely differentiable inverse. Diffeomorphisms provide the right notion for two smooth [[manifolds]] to be "the same": if there exists a diffeomorphism, between two manifolds, then they will have all the same [[topology|topological]] properties.
A '''diffeomorphism''' is an infinitely [[Derivative (calculus)|differentiable]] [[homeomorphism]] with an infinitely differentiable inverse. Diffeomorphisms provide the right notion for two smooth [[manifolds]] to be "the same": if there exists a diffeomorphism, between two manifolds, then they will have all the same [[topology|topological]] properties.
Put another way, a diffeomorphism is a type of function that satisfies the following condition: both the function and its inverse have continuous mixed partial derivatives of all orders in neighborhoods of every possible point.
Put another way, a diffeomorphism is a type of function that satisfies the following condition: both the function and its inverse have continuous mixed partial derivatives of all orders in neighborhoods of every possible point.